The doctor prescribed medication to correct an issue. Failing to follow the doctor’s order is failing to follow an order and if she gets sick again she has caused herself injury. Either way both actions are most likely punishable under UCMJ. You mentioned AT so I am assuming you are Guard or Reserve. Was the doctor a civilian or military doctor? If he was a civilian, you need to send her to a military doctor as the military usually does not recognize civilian orders. The military doctor will then put limitations into a profile. If it was a military doctor the prescription is an order!
Drinking is a privilege that can be revoked by the commander. The commander could revoke her drinking privileges during the AT period, especially if it has adverse effects on her body as a result of the medication she was ordered to take.
You could give the Soldier a counseling statement and order her to continue taking the medication. If she states the medication is making her sick, send her back to sick-call. You can recommend in the counseling that the commander suspend alcohol privileges as well. You can also state that failure to obey an order is punishable under UCMJ
You might want to run this by your JAG as well.
Read The Mentor: Everything you need to know about leadership and counseling for more information about Counseling, Leadership, Corrective Training, and Separations in the Army.