Should Celestone be injected into my back to reduce swelling caused by degenerative disk desease?

This from http://www.niams.nih.gov/Health_Info/Back_Pain/default.asp#10a (this is an excellent link packed with lots of good accuarate information)

".....Injections: When medications and other nonsurgical treatments fail to relieve chronic back pain, doctors may recommend injections for pain relief. Following are some of the most commonly used injections, although some are of questionable value:

Nerve root blocks: If a nerve is inflamed or compressed as it passes from the spinal column between the vertebrae, an injection called a nerve root block may be used to help ease the resulting back and leg pain. The injection contains a steroid medication or anesthetic and is administered to the affected part of the nerve. Whether the procedure helps or not depends on finding and injecting precisely the right nerve.

Facet joint injections: The facet joints are those where the vertebrae connect to one another, keeping the spine aligned. Although arthritis in the facet joints themselves is rarely the source of back pain, the injection of anesthetics or steroid medications into facet joints is sometimes tried as a way to relieve pain. The effectiveness of these injections is questionable. One study suggests that this treatment is overused and ineffective."

In answer to your question Celestone (Betamethasone - a steroid) can be injected into your back for pain relief although its value is questionable.
See also http://www.medicinenet.com/degenerative_disc/article.htm