I had that experience. I don't know any reptile vet where I live, so I read about
the medication to cure RI. It's called Enrofloxacin. I went to a vet asking for this
medication and luckily the vet can estimate how much to give based on weight.
I had to force open the turtle's mouth to administer the medicine drops. I had no
problem keeping the water temp warm (about 80°F or a little more) as it was quite
warm where I live already. After about a week or two, the turtle showed improvements
and from then on, it's living healthily.
Enrofloxacin is a wide-spectrum antibiotic usually given to dogs or cats, if I remember
correctly. Search about it online for more information. Any vet should carry it
in his/her medicine stock. The tricky part is the dosage to give to a small turtle.
Here's my thread when I needed help regarding RI.