Thanks for your question. Is there any dribble of urine that you can see? Is she eating / drinking normally?
Thanks for your answer. It is possible that she has bladder stones that are blocking her unrination, although this is much more common in male cats then females. I think it is more likely that she has cystitis, or a urinary tract infection, and this causes a burning sensation that makes her feel like she has to "go" more. She is not producing a lot of urine at one time because she is using the litter box so much, so it's only coming out in dribbles.
Her otherwise normal attitude with normal eating / drinking behavior tell me she is stable enough to wait until tomorrow morning and is not in any immediate danger. At that time your vet will perform a urinalysis, possibly some x-rays and blood work, and prescribe some medications to help her out. If cystitis is confirmed as the diagnosis, then she will most likely be on a cycle of antibiotics. You can also ask your vet about some mild pain medications to get her through the first few days, as it takes a while to see improvement with the antibiotics. It is a burning, uncomfortable sensation, but it is not severe pain.
Good luck, I hope she is feeling better soon!