Anti-inflamatories are NOT what should be used for chronic pain, it interrupts the healing cascade and actually slows and even halts healing. Sure if your a couch potatoe its one thing but if your athletic your setting yourself up for long term damage, often irreversible.
A few things come to mind when you talk about muscle/tendon/ligament pain. Muscles are very vascular and heal quick if allowed to. Tendons and ligaments on the other hand have a very slow cellular turnover rate of 300-500 days and little vascularity making them slow to heal.
First things first your body needs the nutrient to repair damage. Collagen based tissue (ie tendons/ligaments/skin/cartilage/arteries) all require a vitamin C based enzyme for proper healing. Vit C (in the form of ascorbic acid) at 5+ grams a day can do wonders for healing collagen based tissue. Add in some lysine, proline, MSM, chondroiten and you have a powerful weapon against collagen based damage.
Next pain can come from "short circuiting" nerve cells often due to lack of one or more of the B vitamins, specifically B12 and folate in the forms of methylcobalamin/dibencozide and methylfolate respectivly.
Most B12 supplements are based around cyanocobalamin which is worthless and the b9 used is often folic acid which is worthless as well.
people who get too much D, not enough A and not enough K often get calcium buildup in soft tissue, this can cause pain/aches etc.
Potassium is low in almost everyone I have every questioned. Rarely do people get even the paltry amount the FDA recommend. Athletes due to sweating more and exercise require much more than the paltry 4800mg recommended by FDA. Potassium supplementation alone has helped many of my aches and pains as well as having improved my endurance.