I work out 4 times a week, but for the past few days I have been getting chest pain on my right side. Starts from the underarm all the way to the upper right chest. When I push my chest and underarm with my fingers it hurts. Breathing is not really a problem. I don't know what it is. Please advise if I should seek a doctor or is it just a pulled muscle.

It may very well be a pulled muscle, but only your doctor can diagnose this. Although breathing is not a problem (that is good) you should still seek the advice of your physician. S/He will need to examine you to know for sure exactly what this is.