I can suggest a few different things as I have basically adapted my style of bowling to not have this happen. As it plagues me every now and again.
There are various things you can do to reduce tension or muscle activation in your swing or ball fit that can help reduce this problem. As Dennis mentioned, keeping your arm straight and not letting it bend is a big contributor that can remedy some of the pain. Not clenching the ball in a death grip can help as well, especially if you are swinging with a bent elbow.
As for pain, an elbow/arm band or brace can help. Massaging the side of the forearm that connects to the part of your elbow in pain (pro tip, it works for your wrist as well). Acupuncture can work but it does not treat the cause, same with the massaging.
Typically, this affliction is the result of a muscle imbalance between the prone and supine forearm muscles. So keeping your arm stretched out and working specifically to target and strengthen the part of your arm that is imbalanced will help the tendon and ligaments grow in strength and handle more pressure or weight. Also DO NOT, I repeat DO NOT, expect this to be done quickly. Connective tissues take much longer than muscles do yo adapt and grow. It took me nearly a year to get my elbow in a manageable spot while I retooled my bowling and worked on the muscles.
A small exercise I can offer is to get a container like a large protein shake mix container and fill it nearly all with sand. Stick you hand in inside the opening and then open it up. Then lift the container 3sets of 10 times. It may not seem like a lot but it is a process. Make sure you do it over something you don't mind getting sand on or dropping a container on cause it may slip off. 👍
Hope that helps,
The Demolition Man
Be like water making its way through cracks. Don't be assertive, but adjust to the object, and you shall find a way around or through it. If nothing within you stays rigid, outward things will disclose themselves.