Sometimes I feel as if my heart is skipping a beat, itll feel really shallow for a second and I feel short of breath. Is this normal?

Sometimes. What you feel (palpitations) are due to extra systole (extra heart beats coming from top or bottom heart chambers). All normal people have them, but not all can feel them. If they become prolonged (20-30 sec at a time) or cause chest pain, dizziness, passing out, you should obtain an event or holter monitor to evaluate for sustained arrhythmias that may require treatment.