I'm not a doctor or a nurse, and if you asked a doctor or a nurse they would tell you to get it looked at right away because that's what they will always say when there is any sort of chest pain involved. They have to for liability reasons. However, there are very many reasons why people feel chest pain and they are usually caused by something simple, like tension in the muscles, or muscles getting pinched in the ribs, or a pinched nerve in your shoulder or something like that. What you are describing sounds very much like muscle tension to me; have you tried relaxation techniques and massaging the area? If the pain is worse when you press on it, then it's almost certainly muscular-skeletal. If it doesn't, then it may or may not be muscular-skeletal. If massaging it helps, then it' a safe bet you are not having heart problems. Heart attack pain is described so many different ways that it's pretty much impossible to diagnose even the likelihood that this is the problem based on someone's description of their pain.