Sounds like you could have IC. I am the same way. No pain just having to go all the time, even when I limit my fluid intake. I go about 15-20 times a day and about 2-4 during the night. I literally only feel comfortable when completely empty (not joking).
My urologist started me out on Bactrim as well at first just incase it was a low grade infection. All my lab work comes back normal and negative for UTI, except the PH level I think comes back a little high for her liking.
Give the Bactrim 10 days to work, if not, go back. The way I was diagnosed with IC was done by having a cystoscopy done. The ironic part is that she put me back on Bactrim and I have been on it since October 08. The symptoms are still here, so in my opinion it is not helping me, but I do what the doctor tells me, although it did cut down on my frequency from 40 to about 20 times. I also apparently have a slightly fallen bladder, i did some kind of flow test on that one. She wants to do some kind of minor surgery to lift the bladder, i think it is like some kind of "stir-up".
If you still have the problem after a 10 day course of bactrim, go back and get other tests done.
The question is, what is your diagnosis? You clearly have bladder symptoms, but frequency and urgency and a heaviness sensation could be a UTI, IC or overactive bladder. To make the diagnosis of IC you need a negative urine culture and urinalysis during symptoms, plus pain/pressure/discomfort (heaviness),urgency or frequency. You also need a pelvic exam by a gynecologist to rule out significant prolapse as the problem. You may have IC, as it is often difficuly to diagnosis initially, and is often confused with the other problems noted above. You need to see a gynecologist or Urologist who specializes in pelvic pain/IC to sort this out. Start with the urine culture off antibiotics, pelvic exam and go from there. Good Luck