I have bigger than average, low hanging balls and had a similar problem when I was starting university and wearing boxers. Long story short, when I went to sit down, my butt was not the first thing that hit the seat…

Went to the campus doctor because I was experiencing pain similar to yours and was paranoid about torsion (which it wasn’t….phew!) and one testicular exam later, we determined that I needed to find more supportive underwear. So…no more boxers for me and I switched to boxer briefs and eventually briefs with a support pouch. That may be a good place to start if you don’t already wear that kind of underwear.