Regrettably, this doesn't really help since every turtle mentioned so far (except the red-belly obviously) and more all have yellow bellies.
Yellow-bellied sliders are generally all dark brown/black with thick, yellow markings, even as young turtles. However, pattern and color varies, so I'm not ruling out a yellow-belly.
Red-Bellied turtles are now very rare in their native range, almost to the point of being endangered. I know they're protected in Alabama (being the state turtle there). Either way, I think we ruled that one out.
Painted turtles, like I said before, are usually not that nicely patterned. Here's a pic for comparison.
My vote still remains on a cooter of some kind. There's about 6-7 different species. Knowing what area you're from might help determine which you might have. Here's some pics of babies and a couple adults.