I am guessing your in teh States or something, as if your In Australia, its getting colder, and the shows are nearly over.
I would suggest letting her outside on a nice hot days, and let her roll. This helps remove the hair to be shedded.
Anotehr good way is to use a curry comb and a shedding blade. Use the curry comb on her legs and places that are ticklinh or need special attention, use the blade for her belly. Use them every day, even twice a day.
Wash her and remove the water using ablade, then let her roll around and relax. The water helps to lossen the roots from the skin and also makes them feel 'too' clean,. and want to roll.
If that doesn't work, and im guessing your riding and haltering. In riding this owuldn't matter as much, as the saddle and your legs would cover most of it, but in halter, you might have to rub it out.
At mid after noon, when the weather is the hottest, go out and grap the tiops of the hair and pull gently but sharp, thsi can be done with almost every hair part, though grab more than one, or it will take you years. A bunch would work, and the heat helps to loosned the folicals.
Use Oil products, black sunnies, or some Cod Liver Oil, oils help to remove things form teh body, my horse was sick and we had to give him 5lt of Parafin, ot began to come out in his coat, ands it supper shiny and it was really fine, now its coming into winter, he's getting heary and warm.
Only use a cap full, if your mare is over 15.2 then use 1 and a half, build up gradually. Dont use too much oil products, if you use Cod Liver, dont use Black sunnies and vice versa.
Re: the anti biotics, it would only have afected her then, it is way out of her system, if you still tink its the treatments, use a hernal mix like garlic, rosehip and camomile, this not on.,ly helps to improve coat (Rosehip) and improve hoof (Rosehip) and healp maintain a healthy digestive system (Camomile) and to help fight infection (Garlic) it also helps to flush any bad things out. The camomile helps to keep the bowels running in order, and i use it for my gelding and will probably use it all his life, as well as the rosehip and garlic. Its helps them inside and out. The herbs would also help their coat, there is also a herb good for their coats, and improves the shine and condition. This may be beneficial, but enquire about what herbs you can use together, i know rosehip, camomile and garlic are good tegether, and i thinkthey are the only ones you can combined safely. But enquire to be sure.
I ope this helps and good luck.
I ride Appaloosas so i know about the paints!