Prednisone is a steroid. Steroids are contraindicated with Lyme/coinfections.
Well, not entirely. Small doses can be useful for treating disruption of sleep or blood sugar or electrolytes, which comes from dysfunction of the hypothalamic-pituitary-adrenal axis.
If you've got muscle or joint pain, it's probably because the bacteria got in there. The only way steroids would help that is if you took enough to suppress your immune system, which you don't want to do.