Yes, Xanax can slow you down, breathing included. But it would depend on how much you were taking, how often you took it, and perhaps how susceptible you were. I have COPD and use Xanax only as needed and at the lowest dosage. It does not affect my breathing, and perhaps because of its calming effect may actually make me breathe more easiiy.
My guess would be the xanax from looking at the side effects. By the way, an anxiety attack can effect your breathing too. I would start by talking to the doc that prescribed to xanax to you. Hope this helps.