Hello~It is always a good idea to take a good, high potency pro-biotic when on long-term antibiotics as the antibiotics tend to remove the "friendly" bacteria from your gut, thus sometimes causing issues like thrush, or candida. You can get the pro-biotics from most health food stores, make sure they are the kind that are refrigerated and have high amounts in each dose.
Well, I'd imagine your doctor wouldn't give you something that isn't safe but DO understand your concern. Did he swab the white stuff? Is your throat sore or the white stuff is just there? I was on long term antibiotics a while back for a tooth issue. I took antibiotics for a full month around the clock. A couple weeks after I was done, my GI tract went nuts. I was really sick at first with diarrhea an pain. I thought I had c diff to be honest. But it got somewhat better although I had raging diarrhea and odd stools for a month. I used exactly what SassyLassie says, probiotics. I took it regularly. And I learned about something called "prebiotic" which you also do. That's things like pickles and sauerkraut. (yep, that kind of thing. Apple cider vinegar too). I also drank kambucha tea. All set you up for the probiotic to do their thing and multiply your good bacteria. It took about 3 plus weeks to get back to normal. All as a result of depleting my gut of flora when on long term antibioitics. So, prepare for that. Eat greek yogurt with live cultures too when on the antibiotic. good luck