What is a good over the counter pain-killer that won't cause me internal bleeding

No over the counter pain medicine will cause internal bleeding in a normal healthy person. People who are susceptible to bleeding should avoid NSAID's which can cause a peptic ulcer which can lead to a stomach bleed, as well as aspirin, which causes the platelets to not clot as well as they normally would which will not make you bleed per se, but will increase the amount of blood that gets out by decreasing the clotting time.
In short, avoid ibuprofin (advil) and aspirin (bayer). Take paracetamol/tylenol.

You could try Acetaminophen (Tylenol), it contains no ASA (Aspirin), thus it should be safe for your stomach. It usually quickly relieves pain. http://www.tylenol.com/

I don't know the best but i would try Bayer Advanced Aspirin
If you need a better answer faster i would go to www.webmd.com
Thanks