I did the exact same thing about 1/3 of the way into last season's winter league. Heard a terrible POP and bad pain in my bowling shoulder. Went to my regular Dr. and then to an Orthopedic surgeon who said the same thing as yours. Take it easy for awhile and then resume bowling.
Your bicep muscle will eventually droop and look kind of funny but amazingly enough you can still bowl. It did not affect my game at all. Doc said if I was a younger man and needed my right arm strength to earn a living he would operate, which takes many months to heal properly but since I am an old phart and retired it did not make much difference.
I did switch my arsenal to 14 lbs just in case it was easier but do not see any difference in my strength or anything related to bowling.
Give it a rest for a couple of weeks and be careful but you should be OK.
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