You're on the right track moxsum. Probiotics. If I were "forced" to take antibiotics, I would definitely take probiotics and prebiotics. Prebiotics will feed the flora. That is what they live upon. Rice bran, oat bran, inulin. https://en.wikipedia.org/wiki/Prebiotic_%28nutrition%29
Rice bran is the easiest. Less allergenic, gluten free.
For probiotics, don't forget the fermented foods - yogurt, sauerkraut, miso, kefir, ...
Yes, the probiotics are in other places than your digestive system. You nasal passage will have them, unless they have been wiped out by fungi. Your immune system will be repopulated in time.
Another thing I would do in that circumstance would be to take adaptogens; such as ashwaganda, schisandra, licorice root, and others listed here. https://en.wikipedia.org/wiki/Adaptogen
Seaweed (kelp) will help your entire endocrine system too.