This pain is not typical of pain from angina or lack of oxygen to the heart. Unless there is damage you will probably have a normal EKG at the hospital. At your age it is unlikely to be a cardiac event. Pain with a cardiac etiology is not positionally relieved.
Cardiac enzymes only show when there is cellular damage/destruction secondary to hypoxia. In other words an infarct. That is usually also reflected in ST changes on the EKG.
A more likely cause is inflammation of the pancreas, or, in a worst case, an aneurysm.
In the case of such pain the answer is not to "see a doctor", but call 911 and go to the nearest ER.
As odd as it sounds, it could be heartburn brought on by the fatty food. That's the best case scenario.
It could be -- heart attack (very mild), angina, or it could be back pain.
It could also be anxiety or a panic attack.
What I suggest you do is go see a doctor. They'll run an EKG to see if there's anything wrong with your beats and they can do a blood test to see if you have any Cardiac Troponin, Creatine Kinase, Creatine Kinase - MB, or myoglobin. If you have very high levels of any (specifically Troponin), it can actually tell if you are at risk of having, or have had a recent heart attack.
Troponin is a molecule that blocks contraction. During a heart attack, that troponin gets released on a much larger scale than normal. When those ranges are above a certain number, it can be helpful in diagnosing your condition.
But, there is a half-life for Troponin in your blood, which makes it important for you to see a doctor as soon as it happens, or at least within the same day.
If you EVER have chest pain, you need to see a doctor. If it happens next time, take an aspirin and head to the ER.
I hope this helps.