How can you tell the difference between anxiety chest pains and heart problems for a heavy drinker?

See doctor. You can't, but your doctor can.
Formal Evaluation. The problem is that heavy alcohol use may result in many real problems that may be manifested in many ways, some of which may be ostensibly cardiovascular (including chest pain). Anxiety can be seen in heavy drinkers for a variety of reasons as well. Since one cannot reliably determine is any symptoms are psychological versus physical, a formal cardiac evaluation would be prudent.

Related Questions

Just had another check up today and Drs still can not find why my left arm bp is higher than my right. Difference of 20-30. Right 110-118 left 130-150. No heart problems and blood test perfect. I due get chest pains.

There should be a. relatively simple answer. You just have not had the right test yet because the Drs are avoiding invasive tests like angiography. Blood tests will not reveal the answer, you need imaging studies. CT or MRI of thorax. Or angiography. Ultrasound might potentially show something.
Anatomic issue. Think coarctation or subclavian artery syndrome. Go see a good cardiologist and discuss with him.