JohnN,
In my opinion, warmed up muscles rarely get injured in bowling. Anything that you can do to warm up the affected area is a good thing. The sleeves can aid with that.
What do most bowlers do before the practice time starts? They eat pizza, drink something, yak with teammates, (virtually anything besides stretching their legs, shoulders, forearms, wrists and fingers). When the lights turn on they go after those first few throws with full force and then complain later that they injured something.
When you get to my age and have had countless sports injuries, and a shoulder reconstruction surgery, you start to realize how important a few minutes of stretching and warm up are. I'm guessing you injured yourself at the base of the bicep, where it goes into the elbow. Sometimes it's a tendonitis, and hopefully not a tear. Either case will require some rest and ice to help with internal swelling. You'll probably be fine and back to throwing strikes soon. Good luck to you.