"I do not see a need to go to a doctor and spend money on something that only bothers me while bowling and maybe a day or so after. "
So instead, you come onto BR looking for in-depth orthopedic medical advise......
The shoulder is a complex joint. A thousand different things could be causing your pain. The fact that it isn't going away over time by itself should set off some red flags to get some specialized diagnosis.
I currently have some serious shoulder problems with symptoms similar to yours that are preventing me from bowling right now. Go to an Orthopedic Specialist and get checked. It doesn't automatically mean surgery. The money you're spending on bowling will cover professional diagnostics, so don't be cheap. Take care of yourself for the long haul.