Hi, welcome to Neurotalk.
As Agate pointed out, your medication has the potential to cause itching and so does your type of arthritis. I would ask your Doctor again about this. Are you seeing a Rheumatologist? If the itch is accompanied by a rash, it needs to be looked at right away. I am on a pro-inflammatory medication. It causes "flares" as well and it also makes me itch. If it gets too bad I have been prescribed antihistamines. Ask Doctor about that.

The flares themselves could be a rheumatoid arthritis flare. In an autoimmune disease, flares can be brought on by many factors including stress, over heating, certain foods. You would know all this already I'm sure.

You could try to reduce inflammation by making a change in diet. The site below mentions triggering foods and other toxins even airborne. It's specifically related to the spine but it also gives suggestions on how to manage and prevent RA flare.

Spine Universe -Managing RA flares

I'm sorry you're in so much pain and the itching can be unbearable I know. Please talk to your RA specialist about treating that itch.