Drugs are bad, well, some of them

I suffer with migraines and headaches daily. from the moment I wake to bed time. been almost 10 years of this. it sucks. hopefully you find relief and a fix for it

Go with the drowsy and do a medical withdrawal from school.

I'd tried to power through a finals week and it ruined my GPA. Now, look at me! Tell your parents they're going to need to support you financially through this or you'll end up an FML troll!

My dad suffered with this for decades, the only option open to him was ECT which left him with epilepsy after a botched stay in an asylum in South Africa in the mid seventies. I have the same condition and living in the UK means that taking the drugs means I can't drive or cycle without endanger myself or others which means I have trouble finding work. Push through the pain get your exams out of the way and take a few months off to recover.

Request extensions on medical grounds, gives you more time to prepare

How about taking half a dose of medication? This way, you will still have headaches, but they will be tolerable, and you can focus enough to ace your finals. Also, it would allow you to stay awake while you wrestle a prescription for better medication out of your doctor.