Hello Paranoid Girl,
Welcome to Healing Well. I'm sorry that you're experiencing so much pain. Unfortunately I am also often woken up by migraine headaches. It is not uncommon for over the counter medications such as Tylenol and Advil not to take the pain away. Migraine headaches are different for everyone and it takes different medications to help different people.
Migraine headaches stop your stomach from absorbing medication which is why the medications often don't work. There are special medications created just for migraines called triptans. Examples are Zomig, Imitrex, Amerge, and many more. These come in injections, pills, rapidmelts (melt in your mouth), and inhalants. If one is having trouble with their stomach trying an alternative to pills often works.
Sometimes taking an antinauseant (Gravol in Canada) with your medication can settle your stomach so the medication can be absorbed.
The neurologist is the best person to see, especially a neurologist who specializes in headaches. When you suffer from chronic migraines, the neurologist will generally prescribe a medication or combination of medications that prevent your migraines. The neurologist will also generally give you rescue medications for when you do occassionally get a migraine such as a triptan.
Good luck and let us know how it goes at the neurologist.