"promised her some draughts"
Draught
Creative Commons AttributionDraught - Credit: Jennie Faber, Flickr
Pharmacy
Creative Commons AttributionPharmacy - Credit: Spigoo, Flickr

Draughts were the potions or medicines made and supplied by the apothecary.

Apothecaries were paid for the medicine, not for their advice or time, so they would usually offer draughts for any and all ailments, in excessive quantities.