My daughter had a UTI when she was 3, so it's not totally uncommon. We had just spent 2 weeks at the beach and a lake, so I think all the wet bathing suits had something to do with it!
It does sound like she's still having some pain, especially in the bath. You might try using a hand-held shower while she sits in the tub. Did this all happen when she had the UTI, all at the same time? Did she go on medication? Has the UTI cleared up? If so, the pain should be gone. Putting cornstarch powder on my daughter helped with the irritation.
Being in a wet diaper will only irritate her skin more and will not help the UTI. If you can, I'd try to put her in thick, absorbent undies at home during the day. (like 2 pairs of boy ones - they are thicker and softer than girl undies!) That way, when she pees in them, you can immediately change her and she can't sit around in a wet diaper. Or let her be naked. It may be the right time to potty train, since she doesn't want diaper changes anymore. My son trained before he was 2, so it's not too early.
Um - I may be WAY off base here, and I don't know your childcare situation... but has it occurred to you that she may have been hurt (touched inappropriately) by someone else during a diaper change? I don't want to freak you out, but I just can't help wondering and would be thinking about that possibility if it were my daughter. (I hope that's not the case.) Or maybe she just had a bad experience with diaper changes at childcare? Maybe they used a cream on her that burned? My son was very sensitive and the regular diaper creams would burn him - he'd scream and cry. We switched to Dr. Browns... it comes in a little tub and we got it at CVS... and that was much better for him. Good Luck.
Actually, I was wrong - it is Dr. Smith's Diaper creme.