Hello, and thanks so much for reaching out with your questions! I took Humira for about a year and then switched to another biologic (Orencia) because the Humira was not effective enough for me. However, I did not experience what you are experiencing, an uptick in symptoms shortly before needing your next dose. Rather, my symptoms never diminished as much as my doctor and I had hoped.
I agree that sounds very strange that your doctor is saying the pain isn't from RA. Is he a rheumatologist? If so, I encourage you to consider getting a second opinion, and if not, I recommend you find a rheumatologist. It can often be difficult to find rheumatologists, so I'm including an online tool for locating rheumatologists: http://www.rheumatology.org/Directories/Find-a-Rheumatologist.
Rheumatoid arthritis is notoriously painful, so I'm very surprised to hear that your doctor doesn't think it is your RA that is causing the pain in your hands (if he was offering a different diagnosis or referring you to another specialist or for additional tests that would be one thing, but just saying it isn't from RA is indeed a head-scratcher). While you try to navigate seeking a second opinion and/or altering your current treatment plan (there are several other biologics and other options aside from Humira: https://rheumatoidarthritis.net/treatment/drugs-and-prescription-medications-for-ra/), this article with suggestions from on community members on managing pain may help: https://rheumatoidarthritis.net/living/community-ideas-managing-pain/.
When I'm in a flare, a dose-pack of prednisone or methylprednisolone can be a lifesaver. I have lots of mixed emotions about taking these corticosteroids (here's an article I wrote about the pros and cons I experience: https://rheumatoidarthritis.net/living/the-predni-zone/), but they can make the difference between getting on with my life and being laid up in bed from the pain. If your current doctor has not prescribed a corticosteroid or suggested altering your current treatment plan, these are things you may want to discuss with him.
Please let us know if you have additional questions! I know how difficult it is to experience excruciating pain on a frequent basis, and I want you to know that we are here for you!