Over the past decade there's been a notable "boom" in the alternative medicine market, specifically focused on finding alternative pain relief for everything from chronic arthritis to menstrual cramps to cancer. While I can't specifically speak to the last two from personal experience, I can describe in detail the benefits and drawbacks of alternative pain relief when it comes to arthritis, tendonitis, and joint pain in general.
The first thing to understand when it comes to alternative pain relief is that most techniques and methods - the ones that work, anyway - at there core rely upon the very same principles as tried-and-tested drugs, prescriptions and training techniques. The goal, whether using herbal remedies or some chemical concoction made in the labs of New Jersey, is to alter or improve your body's bio-chemical, bio-physical reaction to its natural processes.
In the case of arthritis, the natural processes of the body are actually out of whack. Be it osteo-arthritis or rheumatoid arthritis, in either case your body is producing too many red blood cells, cells that tend to congregate in your joints causing swelling and pain. The goal of any therapy or alternative pain relief program, then, is to not only treat the symptom (by increasing flexibility, blood circulation, and range of motion), but also to treat the cause.
The way to do that is to focus on the food you eat and your daily exercise regimen. It's important to understand that the old cliche "You are what you eat" isn't just a cliche, but it's a bit of a truthbomb. Certain foods like sugars, alcohol, red meat and the like, have properties that increase your body's producting of inflammatory agents. If you eat a crappy diet, you're more likely to have aches and pains.
So your initial step in alternative pain relief is adjusting your diet. Work in more fresh fruits and vegetables, especially green leafy vegetables like spinach, lettuce, broccoli and the like. Avoid foods that are high in fat (You can have some, but moderation is the key - your body evolved over millennia to eat stuff like fruits, berries and nuts, not cheese and beef jerky).
Your next step is to adjust or improve your exercise regimen. Jogging is good since it's a great cardio work-out that will get your blood flowing throughout, but at the same time it is a high-impact exercise. Ride the bike instead, or better yet, go swimming regularly. When it comes to an all-around workout, swimming is the absolute best. You'll burn the most calories, build the most muscle, elevate your heartrate, and increase blood-flow to all your extremities. All while putting no stress on your joints.