Syncope is the transient loss of consciousness (fainting) and tone in the body that results from inadequate blood supply to the brain. This is a temporary phenomenon and people usually recover on their own in a short period of time.
Presyncope is the feeling that one is about to faint, and it is often experienced immediately before a syncopal episode.
Feeling your heart race, or palpitations, is a very frequent symptom of anxiety.
If palpitations are bothering you a lot, a chat with your doctor is worthwhile. Even if the palpitations are from anxiety, you now have some extra reassurance. If you have been evaluated medically and there is no sign of a cardiac rhythm problem or other medical condition I would look at how to decrease your anxiety.
Please remember I am not a Doctor.