Judging by the therapy you’ve been receiving (antibiotics), doctors probably assumed that your testicular pain is caused by an infection. An infection of the testicle, epididymis, or prostate can cause those symptoms. Sperm and urine analyses are required to confirm or exclude infection. Inflamed hydrocela can also be the source of pain. That thickened scrotal wall can be due to an inflammation that can also cause pain.
Excessive masturbation can cause testicular pain but I am not sure if 5 times per week is excessive. You may stop masturbating for a while to see if the pain calms down.
Certain kidney disorders (stones, infections) can cause testicular pain and the opposite is true as well– testicular disorders can cause kidney pain.
You may continue with the antibiotics as prescribed and you may also take a non-opiate painkiller (NSAID) to relieve the pain.
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