Tylenol (acetaminophen) is okay to take with prednisone. It's called Panadol (paracetamol) in Australia. My doctor recommended the slightly stronger version of Panadol - Osteopanadol - which is a modified release paracetamol that works for longer.

I agree with what @art43 has said. I only need to take Osteopanadol on the odd occasion that the aches are more than usual for some reason, sometimes when tapering or sometimes when I've overdone an activity and the body complains.

There is a post in this thread by edwardh that I will repeat:
https://www.verywellhealth.com/can-you-take-advil-with-prednisone-5095941
I had a friend that was not aware of this drug conflict some years ago, took both, and ended up with abdominal surgery to repair the damage to her stomach.
Suggest you take up the contents of the article above with your doc.

Celebrex