The natural alternatives to these are numerous - many that the public never sees on the OTC marketplace. More familiar analgesics and anti-inflammatories are listed here. There are many formulations/mixtures of various amounts of these:
-curcumin: This comes from turmeric but is so poorly absorbed by the gut that special, high absorption forms have recently been developed. These work much better for mild to moderate pain in my experience, especially better than straight turmeric. (anti-inflammatory)
-boswellia serrata: A form of frankincense often used for chronic arthritis. (anti-inflammatory)
-bromelain: An enzyme from the stem of the pineapple plant. An anti-inflammatory agent (loosens mucus, too).
-white willow bark: "natural aspirin"
-a variety of special enzymes (serrapeptases, nattokinases, etc).
Most of the pain my patients have is due to chronic contraction, muscle tension which itself can have a variety of underlying causes. See my blog on Massage Therapy for further information on relieving this type of pain.