What causes a constant headache?

Several items: Hopefully, you do not possess an expanding brain tumor, hemorrhage, or hydrocephalus. More likely, you have developed "chronic daily headaches", which can involve migraine, or tension headaches, and may be associated with a variety of pain medications. See your doctor, as treatment can break this up.

Anything: You could be having migraines, tension headaches, eye strain or sinus headaches. Sometimes dehydration, lack of sleep/poor sleep, skipping meals, stress, sleep apnea/snoring or chronic sinus allergies can cause headaches. I recommend you see a doctor.