Properly executed, there shouldn’t be much movement in the bow arm. Whether using the swing draw or the rotational draw, the bow arm is held in the same extended position, whether locked or unlocked, throughout the draw. In the final expansion phase, the shoulders are rotated into alignment which pushes the bow arm toward the target, but this is a reaction to shoulder rotation and not an independent movement of the bow arm itself.
The only exception would be if the bow arm elbow needed to be rotated into a vertical position. Many people extend their bow arms with the elbow in a near vertical position naturally, and those who don’t usually end up hitting their bow arms near the elbow with the string, and can be taught to rotate their bow arm elbows into a vertical position. Rotating the bow arm elbow into a vertical position also tends to tighten the triceps, which is desirable and helps keep the bow arm solid.
If you’re drawing with a fixed bow arm, nothing occurs to me that would result in a sore bow arm forearm, other than possibly over-rotating the bow arm elbow, but I don’t see how you could be doing that without being aware of it.
If you don’t have tennis elbow, hopefully your soreness is just a result of some muscle stress from switching to a heavier bow. If if recurs after a couple of days rest and some anti-inflammatories, then I would still suspect tennis elbow, even though you don’t have any obvious hand shock.