@marybarbara, I've heard of steroid injections causing facial flushing but the tablet version I'm not sure. I would definitely run it by your doctor or pharmacist who I'm sure could give a better answer. Here's some information from drugwatch.com:

"Even at low doses, prednisone can cause skin problems. These include skin thinning, acne, hirsutism (excess hair growth), hair thinning, face redness, stripe-like marks on the skin (stria) and impaired wound healing."
-- Prednisone Side Effects: https://www.drugwatch.com/prednisone/side-effects/