Hmmm . . . not that I'm aware. A hemorrhoid is a weakness in the tissue surrounding a blood vessel such that with continued & prolonged pressure (from being constipated and struggling to push out a large stool) the blood vessel starts to expand (think of it as similar to varicose veins in legs). Hemorrhoids can be either internal or external. The latter hurt while the former don't.
However, whether you have hemorrhoids or not really shouldn't affect testicular size. While hemorrhoids are not typically dangerous or a matter of life or death, I'm concerned about testicular swelling. Especially if you're under 40yo, we worry about testicular cancer.
Epididymitis might cause testicular swelling but would be painful. Testicular torsion or twisting of the testes on its axis & thereby cutting off blood supply might lead to swelling as the testes dies from lack of blood flow. However, I'd have expected you to report incredible pain.
However, let's say that rather than the testes itself being swollen, that perhaps another structure in that area is "swollen". Perhaps you have a large inguinal hernia that's descending into your scrotum, especially whenever you bear down to have a bowel movement. Or perhaps you have a hydrocele that still communicates w/abdominal cavity and again enlarges when you bear down. Likewise w/varicocele.
Best thing to do is to check w/your family physician and perhaps obtain an ultrasound of your testes. Oh, and eat lots of fiber, drink lots of water, and get regular exercise in order to soften your stool and minimize straining from constipation. Good luck!
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