I had a cortisone shot in the knee once, too. As you described, it was freakishly painful when the needle went in, then immediately relief from the pain. I also had an injection once in my chin, when I was decades younger. I had a terrible spreading infection from acne cysts. Before I could even protest, the dermatologist stuck the needle in and my horror turned to joy; the pain diminished immediately, the swelling went away in minutes, and the redness disappeared while I watched in the mirror. Cortisone really is a wonder drug -- too bad that's only true under highly controlled conditions.
My knee problem was chondromalacia patella
Chondromalacia patella - MayoClinic.com It got to the point where, in addition to being excruciatingly painful, the joint was nearly immobile. The cortisone fixed it up just like new, but I had to employ some concerted, dedicated changes in order to alter the condition that caused it. Luckily they were do-able, so the fact that my one leg is slightly longer than the other could be compensated for and I have been able to cope since then without a major relapse. At the slightest sign of any inflammation, I get off my feet, ice my knee, and take Alleve. Once I reduce the swelling I'm not irritating the cartilage in a way that creates a chronic condition.
I've never had bursitis but several people in my family have had it in their shoulders from overuse or an accident. They eventually recovered, so I guess for many people it's not a chronic condition. I hope that's true for you, too. I have no doubt the cortisone will speed your recovery. Good luck.