Without getting into the details of your real medication, perhaps you could say you're taking "something" that conflicts with alcohol, in a very casual and dismissive tone like it's no big deal. You can then pick an appropriate ailment/supplement that you feel comfortable with--"Oh, I'm taking this vitamin/energy/headache/flu thing that conflicts with alcohol right now." Just make it sound very dull, so no one will ask you more questions about it.
You could also say you're cutting back on calories, or that X drink has started to give you a headache. In situations like these I think it's okay to tell a lie, when the truth is no one else's business and you aren't comfortable with them knowing.
Also, if someone was nervous and self-conscious about refusing, I think their body language and tone would draw more attention to them. So maybe try (practice?) saying, "Nah, no thanks. Did you see the Oscars this weekend?" in a casual, no-big-deal way.
And, I don't think it's a silly question.
Although of course most polite people would not question or pressure someone, in a group of friends a change in one's habits like this might be worthy of comment or question. Some people might feel it's a comment on their own drinking habits and thus press for a reason. I've also been in a situation with perfectly lovely people who felt that they weren't being hospitable unless they got me a beer or some wine, when really I don't drink much and just wanted to stick with my water. So I think it's good to think about it.