Are you sure of that heater thing? wouldn't it be logical to think that if I turn it off during the night a decrease in temp could worsen his condition?

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Yes I am

trust me, on the early days when I had no acess to antibiotics, I cure some only by that, lots of heat during the day deacreasing at nigth. Thouse keept 24 heat died

About baytril, what is the formula? does it contain peniciline?. that medicine does not exist in Mexico, it doesn't at least under that name but if you gave me the formula I could look for it under another commercial name....
Eurofloxaxin
How did you manage to give your sick turtles that medication and how often did you give it to them?
Its a injectable, only vets can give it. Would also help to know the size of turt
Wait for your input.