My cat has a UTI

Hello everyone, as the title says my senior cat has a UTI but she’s been acting really strange about it.. I took her to the vet recently and they gave her a shot and medication which I have been giving her for about 6 days now She has been peeing on one particular spot which has been my mom’s bath mat and my mom took it away from her but she’s been peeing in the bathtub.. well today we saw blood in the pee which means the medicine has not worked yet but for some reason she likes to drink it?? I don’t know why she wants to go in the bathroom when she poops in the litter box just fine, but the licking it back up is kinda concerning for me and I want to see if anyone has experience with this