Please go see your primary care doctor
. It is generally recommended to go see your primary care doctor at least once a year anyway, especially if you are having symptoms such as the ones you describe.
In an otherwise healthy 20 year old, it is pretty unlikely that the chest pain you are experiencing represents a serious problem. However, it is important nevertheless to rule out a heart problem, and your doctor will be able to do this with a physical examination. If they turn anything up on the examination they may also want to perform some additional testing.
Assuming that this is not a heart related problem, then there are a few other possibilities. The most likely is that you are experiencing muscle strain
or fatigue from the type of exercise you are performing. This can usually be fixed by reducing the intensity of the exercise or changing the type of the exercise.
Side splints are another possibility, as these can sometimes cause significant enough pain that they feel like chest pain. Again, side splints don't require specific treatment, other than reducing the intensity of your workouts.
Make an appointment to see your doctor as soon as you can!