What blood thinner can I take after my carotid surgery if stomach ulcers make it impossible for me to take aspirin?

It depends. Generally Aspirin is still safe in those with a history ulcers so long as acid medications such as omeprazole, nexium, (esomeprazole) protonix, prevacid, etc are taken along with it to prevent recurrence. You should have taken a similar medication to heal the ulcer. If you are allergic to Aspirin or intolerant for some other reason a medication such as Plavix may be reasonable. Discuss with your doctor.
Multiple Choices. Plavix (clopidogrel) is usually the best choice for people who cannot tolerate aspirin.