Plavix has a unique mechanism of action by blocking the amplification of platelet activation by released ADP, and often used with aspirin to prevent the risk of clots for the first year after DES implant. Plavix and aspirin have different mechanism of action to prevent clots. After a year, plavix is usually discontinue as the risk for clots is decreased, and aspirin is continued long term. The risk of a clot is about 3%.
I am on coated aspirin, and that provides some protection against bleeding episodes in the upper GI with no problem. It seems logical the risk of bleeding is greater than the benefit against the probability of a blood clot in your condition based on your health history of bleeding, and plavix should be avoided.
There are substitutes for plavix, but the ani-platelet component remains with all substitutes. You may want to get a second opinion because there are serious implications.