I would be more worried about the mucinex, depending on which type of mucinex, that can tuck you up (not in the good way). I have drank with antibiotics, and I was fine. First time was with penicillin after my wisdom teeth, stopped taking vicodin in the morning (because it was mew years and I wanted to drink that night). Got smashed relatively easily, took maybe half as much as usual, if that. After that, my friends act like it was common knowledge not to drink with antibiotics (no one told me, and it didn't say on the bottle).
Fast forward to this year, I had a sore throat, campus dr says it looks bad, tests for mono, came back negative, so he gave me cephalexin. I specifically asked about drinking with it, and looked online. Couldn't find anything saying that it was bad or that it would make them less effective. The only thing I could find suggested that partying when you are already sick probably won't help you get better any quicker, which makes sense. Went out every night I was on them except for 1 or 2. Felt better soon after starting them was able to drink just as much with minimal effects. My case might be unique, but I would say it is fine. Again, the mucinex is a much bigger concern