What would cause major headaches and sleepiness?

One possibility... Especially if the headache is worse in the early morning, consider being evaluated for obstructive sleep apnea. This disease, which disrupts breathing and sleep, can often cause a combination of headache and excessive daytime sleepiness. Your pcp or a neurologist can help decide if a sleep study is indicated.
Several things. Headaches have many causes. See the list on the picture. I suggest you see your physician and discuss a plan to determine the cause. Your doctor might order imaging of brain and optic nerve exam to rule out serious conditions.
Morning headaches. Headaches on awakening and daytime sleepiness are two common symptoms of obstructive sleep apnea syndrome.