It is okay.
In fact, it is very common for vets to use either steroids or non-steroidals for arthritic issues combined with Tramadol on a regular basis. So, that prednisone for the skin, very well will help the arthritis even more.
The only thing you have to watch out for is combining prednisone (a true steroid) with an non-steroidal anti-inflammatories like Rimadyl, Deramaxx, Metacam, or Previcox. That should never be done.
But Tramadol (pain medication) with a steroid is fine.