It's definitely from holding too tight, and if you're getting it in your biceps as well, it's probably from holding them tight and pulling them towards you.
The suggestion to stop and think about your grips is a good one. Also, if you're holding them down all the time, you're limiting your attacks - maybe let the pass your guard, or set them up to think they're going to pass, and try an attack (triangle) or a sweep from there, or bail to your knees and go for a single/double leg or something?
If you're determined to hold them down, what about arm triangling their head? You won't get a choke doing it from your guard, but you'll control them well.
Grappling should be fluid, though, and any time that you're staying still and maintaining a position, and forcing them to maintain the position, you've kind of killed the game, IMO.
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