What is the best alternative medicine for relieving my si joint pain?

Alternative care. The best medicine is to see a doctor to be examined to find the cause of your joint pain. When the cause is know then you can have the options of treatment that are know to treat the cause.
No best medicine. The thing about medicine is there is no right treatment for any given person. Every person's body and body chemistry is different. Some of the "alternitive" approaches that i might use for a person's si pain are yoga, si joint injections, prolotherapy, radiofrequency treatment as well as a number of herbals that have antiinflamatory activity like, ginger, curcumin, boswelia. See a physiatrist.