I’m not an expert so cannot give advice other than from personal experience with braces but I’d say October is way too long to wait if it’s broken. I had brackets fall off or break (I had ceramic brackets on my upper teeth) from getting caught on forks etc and even if you don’t notice any issues now or the wire isn’t piling uncomfortably there is a reason that bracket was there and your orthodontist would be able to fix or tell you if it needs to be put back on, waiting might add time to your treatment or I can say from experience that a yanked bracket can damage the enamel or leave glue on. Hope that helps and with regards to swallowing it, I think I swallowed some of the broken ceramic and I’m ok, it’s been 10 years but it’s better to be safe than sorry and ask your dentist