I get severe pain in my pelvis and testicles (not always the same one) for several hours every few months. from biking or tighter underwear at times. can arrousal without ejaculation cause this also?

No: These symptoms can be due to chronic inflammation of the testicles or epididymis or prostatitis. A thorough history snd exam should be able to point to the possible cause. Do see your family physician or a urologist got further advice

Yes: Yes. This is so common it even has its own name in the lay public, known by many as "blue balls syndrome".