Mentioned this to my gym coach today and he suggested working on a couple of moves, if you aren't already. First of all, good old bench press, so as to be able to push/lift your opponent off if you're trapped underneath him. Second one is the "Turkish get-up", where you lie on your back on the floor and keep one arm vertical at all times as you get up into a standing position, then go back down & repeat e.g. three or four times for each side.
Here's a short but very step-by-step video showing how to do it, although you probably won't want to start off with a kettle bell!
https://youtu.be/2dx2rM1FSgE
Get the technique right first, then as you progress with it you might start doing it with a dumbbell in the hand you're holding vertically. Again, this is about helping you to resist being held down.