Yeah, see the doctor. Check around for one that doesn't take insurance (rare)-- Why? They're usually a lot less expensive (somebody has to make up the difference between what insurance pays and what things actually cost...)
And, try the usual hot packs on the sore muscles, and if you have an old T-shirt, wear it to sleep with your left arm trapped next to your body (not thru the sleeve). It will speed healing.
When I was younger, I played baseball, and was good enough to be a pitcher (relief). This fix works for all sorts of strains in the chest, shoulder, and upper arm. Then start doing stretches in the morning after you get up- they really do work to loosten up your muscles to prevent this sort of thing from happening to you.
And, my friend; remember- the cemetaries are full of "healthy people who don't need to see a doctor for this silly little thing".
You have stories to write, tales to tell...