If you have sciatic nerve pain, there may be some muscle/nerve issues going on that can cause the same symptoms as a uti. A physical therapist that deals with pelvic pain should be able to help rule this out or help develop a treatment plan.
Sounds like a UTI - which can be treated by antibiotics, I would go to your GP before it gets worse. If no infection shows up, might be IC.
entertain the possibility of a bladder infection. Get a urine culture to see if this is present. If negative, get an evaluation by a gynecologist who can look closely at the area to see if there are any cuts that may explain your symptoms.