A horse, like a acow has 4 quarters but a horse has only two Teats. Each teat has two holes in it and separate streak canals that lead to each quarter. If you horse has normal milk on one side of her bag, then she likely has two good quarters.
Is this mare having her first foal?
The BEST thing you can do is keep stripping the milk out of the two infected quarters. I would encourage the foal to nurse on the good side and strip by hand the bad side. OR you can strip both sides, saving the good stuff and bottle feeding the foal.
Unfortunately, you probably did not culture the mastitic side so you do not know what you are dealing with. Mastitis can be caused by a number of organisms including Yeast and Corynebacterium. Some can be treated.. others not so much. Some can be treated intramammary with some success (usually at drying off), others not so much. Staph is one of the worst to treat. E-Coli can infect the quarter and then when the bacteria die, the let off toxins that can kill the host (mare or cow).
Most organisms are killed by the stomach acid of the foal. HOWEVER, I would want that foal to NOT nurse the bad side w/o stripping until his antibody check was complete and you knew he had adequate IGg.
Talk to your vet. Your mare may have only two good quarters and if she does not make enough milk you will probably have to supplement the foal's intake with bottle feeding.
There is something about the outside of a horse that is good for the inside of a man. ~Winston Churchill
) Dinosaur Horse Trainer