Masturbated last night and a kind of a burning/heavy feeling on the right side of testicular vein. is it normal?

Could be: If you have rough hands with calluses, that could be normal. Give it a rest and see if time heals the area.

Probable varicocele: Best to see an urologist but it sounds like a variocele but could also be something else such as ejaculatory duct obstruction, spermatocele, hydrocele, hernia, std, lipoma, epididymal obstruction or inflammation and of course secondary causes of varicoceles . Between history, physical exam and ultrasound your doctor will be most likely able to accurately diagnose you.