Feeling hard tube above and beneath testicles & it tenders if touched. slight burning in testis veins after urination and swelling in veins.

Nonspecific: possibly a varicosele which is related to cenous reflux esp if it's on the left. May be orchidis or inflammation of the testes. Might be torsion ( twisting) of testes. Need evaluation by md

Here are some...: Most likely, the hard tube above testes is vas deferens and that beneath testes is epididymis. If still in doubt, confirm it with a urologist. How & what you felt - slight burning in testis veins after urination needs more specifics and relevance of all symptoms + physical exam so to deduce possible diagnosis for right care & counseling.