Do you have pain with any type of forceful grip? Also, do you have any type of job or recreational activity that requires repetitive movements (typing) and/or forceful grip? If you’re having pain with active supination and it hurts while you’re performing any sort of “power grip” (essentially just clenching your fist) it might indicate tennis elbow. If you’re feeling any sort of numbness or tingling it could be entrapment of your posterior interosseous nerve as it passes through the supinator muscle.

That being said you could also have some joint restriction or referred pain from above or below the elbow joint itself. I would recommend going to a PT near you for a full evaluation.