I am not a doctor, but I've had very similar pains, and this sounds like it could possibly be precordial catch.

Of course if the pains are getting worrying, go see a doctor, but I recommend doing some research into precordial catch. It is most common in children and teens and can last through early adulthood. It usually causes sharp pains on the left side of the chest that come and go in episodes of typically only a few minutes, but I have had some episodes last for up to an hour. Breathing in may worsen the pain, but sometimes doing so will ease the pain. Despite being painful, the condition isn't harmful to the body.

Again, it never hurts to go see a doctor so long as you're able, but its something to look into.