If getting rid of the disease was as simple as learning magic, the merchant association granddaughter would probably have learned it already. There are two possibilities I can think of that rule out learning magic as treatment:
1. Magical knowledge is exclusive to the nobility, since merchant guy didn't even mention it as a possibility, he just talked about the treatment costs;
2. We know that there's magic in this world, but from what we've seen, magic manifests in very subtle ways or in magic items. Maybe magical energy is something that can't be directly manipulated by humans;