I would think she has some kind of health-problem, possibly a kidney/bladder-problem that’s causing her to drink more. So that it’s all connected. Not that she drinks more due to urine burn, but she drinks more for some reason, she pees more because she drinks more, and that makes her skin wet with urine, and that’s how she got the urine burn. That’s my thinking.
Drinking a lot a lot and consequently peeing a lot (polydipsia and polyuria in medicine-speak) is an observandum in any animal. It may signify any number of health-problems ranging from minor to major. So I really think you should see a vet and bring a urine-sample (if you can get her to pee in an empty litter-box and then pour it into a clean glass jar f ex).
Is she spayed? Uterine/ovarian problems may cause a bunny to drink and pee excessively.
As for flystrike, you have to try and keep her clean and check her hind quarters very carefully every night. If she has any type of open sores it’s not safe for her outside since flies of course love to lay their eggs in open sores.