What is the best way to relieve severe back pain with over-the-counter medicine?

Anti-inflammatories. Otc meds such as Ibuprofen or Naproxen can be very effective in relieving back pain when used regularly for a short period of time. These are usually paired with stretching and strengthening back exercises.
Get eval. Nonsteroidal anti-inflammatory drugs (NSAIDS) can be excellent for this type of pain. They can help with both pain relief and in reducing inflammation. Examples are ibuprofen (like Advil, Nuprin or Motrin), Naproxen sodium (like Aleve, (naproxen) Naprosyn, Anaprox) or Asprin (such as Bayer, Ecotrin, Ascriptin). Avoid NSAID's if pregnant or allergic to them.

Related Questions

What's the best way to relieve severe back pain that is related to scoliosis with over-the-counter medicine?

Well, first know. That most common form of scoliosis does not cause pain unless it is a very large curve or it involves the lower back. If no issues with your kidneys, liver or GI tract like an ulcer & you have no Aspirin allergy & not on any blood thinners then you can take Ibuprofen or Naproxen with tylenol (acetaminophen). Otherwise, you can just take tylenol (acetaminophen) if your liver function is normal. You can try patches like icy hot.
NSAIDs. There aren't a lot of options over the counter, but NSAIDs such as Motrin or Tylenol (acetaminophen) based products are the traditional non prescription medications used to treat back pain, moist heat can also help. Don't hesitate to be seen for a specific cause to your pain.