I just took 800mg of ibuprofen at 7:30am pdt, can i take an aleve (naproxen) 220mg, extreme back pain?

Don't mix these: Ibuprofen (Advil, Motrin), naproxen (aleve) and Aspirin are all NSAID s(non steroidal antinflamatory drugs), and should not be taken together at high doses as a rule. As long as you don't have any liver issues it should be safe for you to take up to 1000mg of Tylenol (acetaminophen) three times per day. For good pain relief try alternating 800mg ibuprofen and 1000mg Tylenol every 4 hours.

Mix it up: Treat the different components of your pain with different medications and modalities. You'll get the best relief. Your back pain comes from irritation of nerves, muscles, other pain generating structures (trust me here) and no one medicine works alone. Add a dose of Tylenol (acetaminophen), apply ice, try some gentle isometric motion (squeeze and release your belly). See a doc if still in pain