Ironically, that's probably the best way to feel better.
The body has 3 primary metabolic energy systems: the ATP / PC system for power, the Glycolytic system for moderate bursts of 30 -90 seconds, and the Aerobic system for providing sustained energy over the long haul. We use all 3 systems continuously, but one particular type is the dominant one based on how quickly we need energy.
Interval training typically works the Glycolytic system the most, and produces the most lactic acid.
Lactic Acid signals the brain to release norepinephrine, a neurotransmitter hormone which is responsible for alleviating pain, among other things.
What does this mean? It means the best thing to do for pain and stiffness is usually more movement, unless the injury is severe.
Interval training in particular can be very effective in creating a euphoric, pain-dulling feeling. If you have arthritis, and high-impact exercise bothers your knees, you could get a natural pain-killing effect from interval training on a bike.
So the next time you're about to reach for a pain medicine, try moving instead.