The doctor ran tests for three things? (Chlamydia, gonorrhea, and trich?) And didn't test you further? (For example, yeast infection, BV, kidney infection, bladder infection, pinworms?) Testing for three things is not a lot of tests.
Point I'm trying to make is that there are lots of things that can make a vagina itchy, and a doctor's job is diagnosis. If your doctor is inclined to give up, find another doctor. In the meantime, don't douche or put anything in your vagina, it can easily make an upset area worse. While waiting for a new doctor appointment, one thing you can do is try eating and drinking foods known to be anti-inflammatory (for example, turmeric tea) and avoiding sugars and junk food. Your body might be able to fight this off on its own.