IMHumO, Rocksor has been giving you good advice.
The only thing different in my mind is the diagnosis. To me most likely these marks are from the heater. Good thing they are clean, not inflamed. In the photo I see no evidence of any other problem, I see no evidence of possible ammonia burn, no ich. The fact that the fish feeds and behaves normally is a great sight that most of its needs are met, albeit there could be latent problems in development, which Rocksor is trying to help you with.
I'd say you have two action items:
[1] remove heater or buy/make a guard for it - can be as simple as taking a PVC pipe and drilling a bunch of holes in it, or buying plastic mesh roll from hardware store and wrapping it around the heater and zip tying - both would be ugly but functional, at least until you get your heater guard; or move the heater into your filter; or get an inline heater, etc.
[2] continue learning the basics of the fish keeping if you'd like to remain and grow in the hobby; start with nitrogen cycle
I will try to very briefly answer some of the issues below.
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I got him solely by accident being told by Petsmart he was a Cory Cat
***That's funny, confusing a corydoras with synodontis
and he would be a good tank mate for my Betta Sunny in an 11-gallon Fluval tank. 5 months later spot was over 6" long and 5" tall from one fin to the other fin expanded. This was a big surprise as he stayed hidden most of the time and barely got a glimpse of a tail here or there for a very long time. I ran out and got him a 36-gallon aquarium and he was a very happy fish.
***Cudos for you! You are obviously a conscientious animal lover.
Just before vacation I cleaned the tank and tank elements
***Bad idea. Could have been lethal. You lucked out.
and noticed he had a slightly milky color in one eye.
***Could be one of the symptoms of too high ammonia level in your uncycled tank.
Googled it and thought maybe he had bumped his eye on the betta log we had floating at the top and he loved to spin and play with.
***Can be, but ammonia is more logical and likely.
The tank was clean and the water parameters were all good and there didn't seem to be any other issues at that time.
***By your measures, which were lacking a lot.
He is swimming well and eating.
***Very good. No imminent danger but doesn't mean he is safe, given how you practice your maintenance and keep track of water. We keep water, not fish! Fish keep themselves!
I do not have a guard on my tank heater as I was unaware they could burn them and had seen him laying on it numerous times. It is the same tank heater that has been in there for months and the temps are normal and steady at 77.4º so I do not know if it malfunctioned and burned him
***Bingo. It needs not to malfunction at all to burn a fish. Sooner or later.
or if it is a disease. (See picture below)
***I don't think so.
I have a guard coming as well as some Melafix and API Fin and Body Cure that will be here today.
***No need for them at the moment that I could see.
Water parameters look fine with the PH at about 7.2, KH being between 80 & 120, NO3, NO2, and Cl2 being 0 or safe, and the GH general hardness being about 500 or less.
***Dip sticks are entirely crude.
I have revived my Betta Sunny once right after getting him as he had an injured gill when we brought him home using the Epsom Salt bath prior to Spot. I have Googled for suggestions but apparently catfish require a different type of treatment
***They do not. Not different enough at all in the first approximation and in the vast majority of circumstances. All dogs and birds and humans of different breeds need similar care within each group.
Any assistance would be so gratefully appreciated please before it is too late.
***It feeds. You have a bit of time to figure out the causes and correct them.
No, I did not cycle the tank.
***Big error for a newbie. Plus you don't know what nitrogen cycling is. Must learn.
He had been in this tank for several months before cleaning it and he was great. No issues
***You lucked out that the tank was large, with lots of surface, perhaps you accidentally seeded the tank too with nitrifying bacteria, and fed little. Most usually this is when people lose the fish at this step.
until I pulled out the plants, washed them well,
***To an experienced keeper this sounds disturbing because you'd might be destroying nitrifying bacteria and introducing harmful chemicals or detergents into the tank.
I am curious though? Where does the ammonia come from?
***Fish breath it out. It is also produced when poop and detritus decompose.
They are fake plants. I used an automatic feeder while we were gone feeding them the same dry foods he has always eaten. I do add fresh and frozen when we are at home. I did opt to only feed once daily instead of twice daily in case it was putting out too much and monitored it for a few days before leaving to ensure he was getting ample food without too much food. Catfish pellets, some veggie pellets, and bloodworms were lightly mixed together in the feeder.
***Sounds great. You are very logical, thorough, and caring. You'd make a great fish keeper.
Why I had cleaned it very well and changed all filter material before we left.
***I'd guess you again destroyed the cycle by doing so.
I will be sick if I lose him though.
***Try to stay positive. I killed thousands of fish in my "care". Of course, I can be used as a counterexample. But aim to learn with each loss.
So how do you suggest I treat him aside from the water change and testing for ammonia? Should I use Melafix? The API Fin and Body Cure? Both?
***I see no need for medicating whatsoever. Currently.
Apparently, these guys get stressed quite easily.
***Not at all. Quite the opposite. Synodontis eupterus and nigrita (featherfins) are fish of steel. And in no small part a testament to the fact that Spot survived so far and even his burns are not inflamed.
Wondering if the stress is not part of the issue
***Stress is #1 killer of any fish apart from accidents and predation.
as I did transfer him to a smaller tank while I was cleaning things out. But it was pretty uneventful. Caught him easily even though this guy is FAST.
***No, no no. That's unneeded stress. This is not how one cleans the tank. You wipe the window and vacuum gravel / sand, etc.
I did burn myself on the tank heater trying to put the guard on. I had no idea they got that hot and since it had been in there for months never dreamed it could hurt anything.
***Yes! They get hot! It is a miracle Spot got so few burns so infrequently.
but I did add the API Fin & Body cure before I read this.

Sorry! I am supposed to dose him 3 more times. Should I continue? I is a Doxycycline treatment and it does not make the water smell or make it too off-color or anything.
***If the wounds are as clean as in the first pic, I personally wouldn't add any meds. Antibacterial meds kill off some of the beneficial nitrifying bacteria, so there are always tradeoffs, no perfect solutions.
He was only the size of my thumb when we brought him home and was sold to me as a Corey Cat which does not get very large. Once we realized how big he was getting I knew that was not correct. I did a search using a picture of him and learned that he was the Featherfin. By April he was a very good size and could not turn around in the 15-gallon Fluval with the decor which they say is the equivalent of an 11-gallon tank because of the built-in filtering system. I loved how clean the built-in filter system in my 15-gallon Fluval tank kept the water but what a pain to clean and it broke when I tried to clean it in April. So I ran out and bought a Top Fin 36-gallon kit that included the PF40 Silentstream Power Filter. I would have thought he would have gotten sick then because it was all fresh. But he was as happy as a clam and loved all of the new room. We also did not put the Betta back in the tank with him. I do believe now he was bullying the big guy. Do you have any other suggestions? Happy to upgrade and improve where needed. I really want the little guy to be happy.
***You are a promising, great fish keeper. Betta are very aggressive to tank mates. I don't know much about them, never kept them, but I'd not add tank mates except female bettas to a male. But I know too little in this field.