I am sorry to hear of your discomfort. From what you write, you sound as if you could have a condition called chronic prostatitis. Prostatitis is an infection or inflammation of the prostate, and it can indeed produce burning pain in your penis like you describe. Chronic prostatitis means it has been there for a "prolonged period". Symptoms of prostatitis which can but don't have to all be present include:
"frequency of urination, slowing of the urinary stream, burning with voiding or ejaculation, burning in the penile tip unrelated to voiding [which you report], sexual dysfunction (such as difficulty with erection), aching in the penis, [again, which you report] testicles, and discomfort in the lower abdomen, low back, groin, rectum or perineum"
It is one of the most common reasons for men to be seen. It is NOT associated with prostate cancer, and there is NO link between prostate cancer and prostatitis. This condition can be caused by chronic or acute bacterial infections, and most commonly, there is inflammation but no bacteria present (but the semen does contain products of inflammation). There is also prostatodynia , which produces pain but no objective findings.
To test for prostatitis, an analysis of the semen is made, which is a different test than the STD tests you said you had and often it can involve a prostate exam as well. In prostatitis, Treatment for this involves antibiotics for a few weeks. Medication can also be given to relax the prostate so it is not as painful.
Here are two helpful websites
http://men.webmd.com/prostate-enlargement-bph/prostatitis-symptoms and http://www.nlm.nih.gov/medlineplus/ency/article/000523.htm
I suggest yet another visit to a urologist, and discuss with him or her your symptoms and the possibility of a prostatitis.
I hope that helps you.