Final answer:
The suggested medication for the patient to begin for her headaches is acetaminophen, as ibuprofen can cause medication-overuse headache.
Step-by-step explanation:
Given the patient's history of daily heartburn and use of ibuprofen, it is likely that her headaches are caused by the frequent and prolonged use of ibuprofen. Ibuprofen is a nonsteroidal anti-inflammatory drug (NSAID) that can cause a condition called medication-overuse headache (MOH) when used frequently and for a long duration. The recommended medication for the patient to begin for her headaches at this time would be acetaminophen, also known as paracetamol. Acetaminophen is a mild pain reliever that can help alleviate headache symptoms without the risk of medication-overuse headaches.