I've been working out pretty frequently with my trainer. last week we boxed and my right shoulder and chest has been hurting for the last week.

Not enuf info: Could be a bruise from a blow or a muscle injury. The former would be tender in a general area. The later would be more discrete over a part of a muscle. A ligament or capsular problem would be near or at a joint. You will know better after another week or two. The joint problems will persist. Try heat and Naproxen until then. Remember to warm up before you work out.