TLDR: It's probably not a heart attack if you can pinpoint the pain, if the pain gets worse on a deep breath, the pain is related to movement of your shoulder or arm, or if it only lasts a few second.

You should call a doctor if the pain is mild but consistent and is untreatable by pain killers, and remains regardless of if you're resting or not.

You should call 911 or get to a hospital immediately if your chest pain is "crushing" or "squeezing," and especially if it is accompanied by ANY ONE of the following: sweating, shortness of breath, nausea/vomiting, pain that spreads from the chest to the neck, jaw, or one or both shoulders or arms, dizziness or lightheadedness, fast or irregular pulse, severe weakness, inability to walk.

So yea you don't go to the hospital for every pulled muscle, but do your best to memorize the above symptoms of escalating seriousness, and you should be ok.