Boyfriend's potential ulcer?

My boyfriend will sometimes experience a burning pain in the stomach which seems to intensify when his stomach is empty. He drinks alcohol generally every weekend, mostly a beer or two with food. When he drinks a lot (happens maybe once a month or so) he will get sick and vomit but with no real concerns. A few weeks ago he had about 3 beers with his friends and did not appear nor claim to be noticeably intoxicated, yet became sick and started vomiting. He had drank on an empty stomach (hadn't eaten anything red or brown) and was vomiting a brownish red substance. I became concerned that it might be blood and in the few weeks since that night he has been complaining of some occasional yet more-often-than-normal stomach pain. I am concerned that he may have an ulcer. I shared my thoughts with him and he seemed to be less concerned than I was and did not want to see a doctor.

Do these sound like the signs of a peptic ulcer? Should I push the matter and try to convince him to get checked out by a doctor or should we just continue to keep an eye on him?