I suspect you mean your drawing forearm. It may be sore because you could be tightening your draw fingers and your arm during the draw...and that may be affected by how you are gripping the string.
Try this: Use only 3 fingers on the string...1 above and 2 below. Hold the string in the first CREASE of your fingers (not on the finger pads), with the tips of your fingers turned back towards you...to form sort of a 'hook' shape with those three fingers. The string should be nestled into that first crease during the draw and your three fingers should be canted at the same angle as the bow limbs (if limbs are vertical then fingers should be straight up and down; if limbs canted 10 degrees than fingers should be canted at 10 degrees, etc.). Try playing with it to get a comfortable feel of the string sitting in that crease and the fingers in line with the bow limbs at your cant angle, then try drawing back to full anchor without releasing just to see how that feels in the hand and on your face. Adjust if necessary so that your face anchor point won't interfere with the three fingers as they uncurl (I like my draw fingesr not even touching my face...only my thunb joint/knuckle actually touches anchor).
I'll bet you'll notice that both your hand and your forearm will feel stronger using this method, your forearm muscles more relaxed and more in line with the arrow...kind of like turning your arm into a rope, with a hook to hold the string. This method of holding the string is called the 'deep hook' and is used by many good archers.
Once it feels good at your anchor then try a few shots close to the bale. Its just a matter of focusing on that black spot on the plate, drawing to full anchor and simply pulling through the anchor slightly at release so your draw hand or fingers don't creep forward (that last part is often called 'maintaining back tension' since you are using your back muscles, NOT your arm muscles, to finish the draw and allow the release).
If your focus is on the spot and the fingers/hand/forearm are kept relaxed with a positive pull-through at release, the string will simply drop away from your relaxed fingers, the arrow should fly nicely off the bow, and that sore forearm (and pinky...the 4th finger that isn't needed now) might just go away.
Try it and let us know how you're doing.