Unfortunately, that's what my IC was like back when I was first diagnosed.
I am also prone to UTIs, and they can be pretty sneaky. I was always coming up as a false negative when I went in to get tested, because my urine wasn't concentrated enough to show a positive result with the dip test. What my doc and I do is this: he gives me urine vials and I have some UTI test strips (for nitrites) at home. First thing in the morning (when infections are most likely to show up due to length of time the urine is in the bladder), I let out a bit and test it and if it comes up as positive for nitrites, I fill the urine vial and drop it off at the lab, then start up on antibiotics at home. You may want to check with your doc to see if you can set up something similar.
It could very well be IC, though. Has your doc mentioned rescue instills to you? When I have that fiery, burns-like-a-thousand-suns IC pain, instills (heparin/lidocaine/baking soda injected by a nurse via pediatric catheter) are like a sitz bath. They are a godsend. I was a bit weirded out by the idea at first, but now they are my go-to treatment when I'm in agony.
Hope you get some answers and feel better!