Would a cortisone injection in my knee help its connective tissue disease pain ?

Only if inflamed: Corticosteroids work best on inflammation. If your connective tissue disease is in an inflammatory phase then it might help.

Cortisone injections: Cortisone injection is a very helpful way to reduce inflammation , thus reducing pain , Depending upon the type of connective tissue u have , there can be other treatments to help the over all process. Place yourself in the hands of a good rheumatologist .