Alcohol is always bad, but of course it depends what kind of sick. You obviously don’t mix it with medicine, because even a single beer could give you a horrible headache.
But also the popular myth that says a drink is good for a sore throat is wrong. Because yes, it does help for a while (as do some alcohol-based syrups, various menthol lozenges etc), but it actually dries your throat which, from the manufacturer’s point of view is great, because you have to stuff your mouth with more lollies. But it just delays the overall process of healing and you could be stuck with a cough for days, even after the actual cold is over.
I was a professional singer for many years and found that the best thing to do at a concert was a simple mouthwash before the event and plain tap water during. Even a sip of wine would make me snore all night and then wake up with a sore throat the next day.