Aspirin, ibuprofen, flurbiprofen and naproxen sodium are some of the nonsteroidal anti-inflammatory drugs available without prescription as of 2015, according to WebMD. Doctors use NSAIDs in treating a wide variety of common chronic pain disorders, such as migraine headaches and arthritis.
NSAIDs lessen inflammation-related pain and swelling by decreasing the body's levels of prostaglandins, which are chemicals linked to inflammation, explains WebMD. Common side effects for the class of NSAIDs include stomach bleeding and hearing problems. The pain-relieving drugs have other side effects, such as increases in blood pressure, kidney disease and muscle cramps. Each drug differs in its side effects.