constipated kitty with high red and white count in urine

My cat has had a bout of crystals in her bladder. She has been on
antibiotics and Science Diet s/d, but she became constipated (because
of the antibiotics?) so she also got some Felaxin. After one month,
she has been switched over to Science Diet c/d (her most recent x-rays
show that the crystals have dissolved) but she's still a bit
constipated. She also has a high red and white cell count in her
urine, which the vet says is a good environment for infection.

So with her latest test results and x-rays, aside from the switch to
c/d, Kitty is still on a low dose of amoxicillin (100 mg) for 30 days
to stave off another infection. She is also still using Felaxin to
help with the constipation.

Does the above course of treatment seem reasonable for her diagnosis?
I'm a little worried about the amoxicillin--if she doesn't currently
have an infection, is it really wise for her to be on an antibiotic?

Are there any other causes for a high red and white cell count in her
urine?

What about the constipation? The doctor said it may also be caused by
dehydration, not just the antibiotics. Our cat sitter says Kitty
doesn't seem to drink a lot of water, but she is eating canned food so
she gets some of her water intake from that. She loves the Felaxin, so
that's not a problem. But I'm a little worried that this may be a
chronic problem.

Any advice?