If I can feel my heart beat in my abdomen and I have middle back pain, could this be an aortic aneurism?

Possible. At your age, unless you have underlying disease (i.e. Marfan's), it's unlikely. If you are relatively thin, it would be expected to be able to feel your aorta pulse.
Could be . Abdominal aortic aneurysm would be very unusual in a 22 year-old. It is also not uncommon to palpate a normal abdominal aorta if the patient is thin.