No need to bother the doc, since you can just run down to the feed store and get a bottle of penicillin. You learned to give shots a long time ago, and an injection of penicillin for a few days will take care of this problem. Doc will sure be impressed with how much you've learned about caring for your horse. It's a good bet that almost every owner has been involved in some variation of these situations. Singling out veterinary medicine is not really correct, since resistant bacteria are rampant among humans.
Human medicine has a long history of over-using antibiotics.
Every child with a minor ear infection used to receive antibiotics. Drugs like topical neosporin and other skin antibiotics are available and heavily used everywhere. There are even adhesive bandages with antibiotic cream built right in. But the bacteria adapted. Now, after countless generations of bacteria having been exposed to these antibiotics, they have altered themselves and are no longer sensitive.