String gauges

I am playing "standard " D'Addario strings (12, 14, 22). To play with my church choir, I need keys such as C, F and now Bb. I started tuning down from D into C and using the capo to get to F. I have never tried tuning up. I use the capo in D tuning to reach G and A. So far I have only needed major scales, and have stuck with 1,5,8 tuning.

This weekend I need Bb. I suspect I can tune down to reach it.

My question is, should I be looking at different gauges to go that low without buzzing? What about up? Can I reach F with those strings?