Actually Doc, If you go and read other forums on here like gerd and acid reflux you will see that it is more common than you suspected, Not to be disrespectful or anything. I just do alot of research when i'm interested in something and my health is very interesting to me.
The symptoms that you are describing of your heart skipping and getting lightheaded are typically not common with heartburn. You could be having some type of abnormal heart beats or an abnormal heart rhythm. I would recommend that you be seen by a Cardiologist before your symptoms are blamed on heart burn. It would help to have you wear a heart monitor (Holter monitor) for a few days or a few weeks depending on how often you are getting the feelings of lightheadedness and heart skipping. Then we can see if you are having abnormal heart beats. Also, it may help to get an echocardiogram which is a study we do to look at the function of your heart and it also looks at your heart valves. This would help rule out heart disease as a cause of your symptoms. The Holter monitor and echocardiogram can be ordered by a Cardiologist.
Hope this helps. Good Luck.