Is it possible for drinking alcohol to lead to acne?

No: Use alcohol wisely if at all, but this isn't causing your acne. It's a non-lifestyle related, non-hygiene related illness with only a marginal link to diet. The key is that you can manage it, though you can't cure it until it goes away on your own. If topical benzoyl peroxide has not cleared you in two weeks, get with your personal physician for prescription strength Rx.