I tested negative for all stds, but I seem to have symptoms of chlymidia, how is this possible?

Yes. . No medical test is 100%. There are always false positives and false negatives. For example, if i go out to your front lawn and randomly pull up one clump of grass and find no weeds in that clump, can i say that you have no weeds in your entire front lawn? Get tested again if you still have symptoms.
Other causes. I don't know what you mean by symptoms of chlamydia, but if you mean burning in the urethra with urination, you have urethritis. It can be caused by many other kinds of infections, including mycoplasma, ureaplasma, trichomonas, reiter's syndrome, herpes simplex and other viruses.