I have been having thumping in my stomach feels just like a baby kicking, but I am not pregnant that I know of. Sharp pain occurs randomly. Ideas?

Peristalsis. Peristalisis is the normal contractions of the stomach and intestines. This may be what you are feeling. The pains are unusual and you should see your doctor to be safe.
Test for it any way. Sounds funny but I have seen or heard of cases where someone is surprised they are pregnant and are ready to deliver. So if you are in the reproductive age and sexually active get a pregnancy test any way. Other reasons for your symptoms i can think if is irritable bowel syndrome. Have your doctor evaluate you.