Okay, this could be caused by a number of different things. We all understand the heaviness and ache telling us it's time to get our rocks off. But, the pain afterwards is more difficult to nail down. You don't say how you cum, only that you do. You also don't tell me how often you cum. This is why it is so important to tell our doctors everything.
So, one possibility is that your balls are being bruised. They're bouncing and banging with either your thrusting, when someone is stroking your cock, or as you jack off. Now, I know many guys love the feel of their nuts slapping against something during sex. But too much of it, or too vigorously, can bruise them. So, the solution here is to ease up on the thrusting or stroking.
The second probability is that the Cremaster Muscles which surround and lift the testicles to push the sperm up into the seminal vesicles are overreacting. They can squeeze too hard, pulling almost to a point where they feel as if they'll crawl right back up into the inguinal canal.
There isn't much you can do about this, though I did read an account years ago (can't find it again) about a urologist snipping a bit of the Cremaster tendons on each testicle. Because most insurance companies will not cover such an "experimental" procedure, guys with over-achieving Cremasters are left to suffer or find other solutions. Try getting a cock ring of the type which will lift your balls away. That may - may - resolve the issue to a certain degree.
You could also try cupping them to hold them down when you cum.
The third possibility is that you're ejaculating a lot - meaning many multiple times per day, every day. Now, as much as we all love the idea of that, too much can do damage. It called too much of a good thing. Having your nuts squeezed over and over again is actually causing trauma to the tissue.
If you try the things I've suggested and still have trouble, you need to go back to your doctor and tell him exactly - in detail - what is happening. You may need a referral to a urologist. Either way, I hope you are able to find relief, because constantly aching nuts is no way to live.
Anyone else have any suggestions?