Great on the adoption ! Turtles are great pets !
Sounds like he had a hard life but all that will change under your care now. From what you described his habitat and diet was all wrong to see the problems you describe. Sounds like he wants to shed but with the retained scutes will be hard and not always in one piece. Will take much longer to do so too. May even with better care still take several sheds to correct over a couple years. Use top header on this page and read all you can on habitat and diets also the different thread under the topics. Get an idea on what's involved in turtle keeping. The more you know will make it very easy for you and him. Best is to offer a good habitat for a turtle and diet and patience on your part. Will take time but shell and himself will get better under your care. Sometimes what a turtle needs and or just wants wouldn't necessarily be what you want to match your home style. Better for him by observing what he wants to make him happy and do what he needs to stay healthy. A good well mixed varied and nutritious diet will go a long way to correct the shell.
The betadine is a surgical scrub , only a cleaner and disinfectant , does nothing for fungus. Was a precaution only by vet maybe so she could see better down the road. You can stop it. Sounds more like shedding and having a little trouble doing it due to it's poor life before you. The vinegar is only for mineral deposit you can also stop that too.
Observe well , offer a good habitat , good diet and in time will see improvements. Do a lot of reading/homework will make it easier for you. Any pictures will help. Can tell more with some photo's. Even if a little fungus just by offering a good habitat with a good basking area along with the shed can help remove any. In nature turtles shed not only to grow but when they have shell problems too. Treatment not always needed but we will see. Read up , in this hobby "prevention" to me is the key !
Example of what you can find on above header :
http://www.redearslider.com/startup.htmlOne does not have to spend a lot of money , make a list and ask questions on what you think you want. We may be able to prevent you from buying something inadequate for your turtle.
On next visit to the herp vet or a call ask for an RX of silver sulphadinze cream that's what treats fungus . Great to have around "if" you ever need it.