What can cause my bottom back teeth to hurt so much after drinking certain alcohol?

Compromised Enamel. Appears you either have a broken down old restoration or new cavities. Could even be a cracked tooth. All need to be seen, evaluated, and treated by your dentist.
Pain. Chances are you either have cavities or fillings that are not sealed correctly. I would suspect old silver fillings that are in bad shape or cavities. You should see your dentist.