Female hamsters can get pyometra (link below). Infection in the womb - can be confused with UTI. Depending on the type, the treatment is either antibiotics or spaying the hamster. At 2 she is probably too old for spaying to be realistically in her best welfare, but a vet could advise on that (some may depend on her condition). I had a minor op/lump removal on a nearly 2 year old male syrian recently - but spaying is a more major op.
Spaying is usually for closed pyometra. Open pyometra (which is more likely in your case due to blood discharge) can be treated with long term antibiotics.
I agree that continuing the antibiotics longer seems sensible and I would suggest to the vet (and mention pyometra).
There is a very good article from a breeder on here (Vectis) about pyometra - it's for Chinese Hamsters but applies to Syrians as well.
It looks into all the dilemmas and may be helpful
Pyometra in the Chinese Hamster - Vectis Hamstery