antibiotics with food on postponed 9 be'av

this year that tisha be’av is pushed until then10th:
A person with a serious ear infection is on strong antibiotics twice a day for a week and has been told to take them on a full stomach. She can take the evening doses before the fast begins and again after it ends, but in the morning will have to do havdalla and eat breakfast before taking the pill. Question is, is there any point in her fasting for the rest of the day once she’s already eaten in the morning?

Yes she should eat when she’s taking the medicine as per her Dr advice. This would be whatever amount of food she needs for the medicine to work. She obviously shouldn’t eat a 7 course meal. Even though she ate, she should fast the rest of the fast.
However if her ear infection is more than just a plain ear infection and she’s not feeling well generally, being that it’s a nidche this year, she should eat. She should still fast for the night, if she can.