Steroids ease inflammation, so it's no surprise that 'general' aches and pains are helped by the course you are taking for your chest. It's also very possible that the effect on your joints will be longer-term - just like the steroids will give your chest chance to heal, they'll help your joints to heal too. Inflammation is a response to injury and wear, but it also interferes with healing - kind of a vicious circle.
14 months ago, I had a bad flare of osteoarthritis in my thumb joint - could hardly move my thumb and the joint swelled to the size of a Ping-Pong ball. I had a steroid injection into the joint and have had few problems since - the steroid allowed the joint to heal.
I can't imagine that steroids would be a go-to treatment for peri symptoms (if someone knows otherwise, I'll stand corrected) - the possible side effects would outweigh their use as anything but a treatment for acute flares of inflammatory disease.
Enjoy the relief, and remember it may last long after the steroid course is finished.