Rheumatoid Arthritis Support Group
Rheumatoid arthritis is a chronic, inflammatory, multisystem, autoimmune disorder. It is a disabling and painful condition which can lead to substantial loss of mobility due to pain and joint destruction. The disease is also systemic in that it often also affects many extra-articular tissues throughout the body including the skin, blood vessels, heart, lungs, and...

Were you given a short dose of Prednisone just to tide you over?
It is listed as a side effect here:
http://www.webmd.com/drugs/2/drug-3441/methotrexate-anti-rheumatic-oral/details
Please see your rheumatologist as soon as possible!
It could be: strain, OA, cricoarytenoid arthritis, or Ankylosing Spondylitis.
I would have an HlA-B27 test run. It is not conclusive for AS, though 95% of all AS patients are positive.
I don't believe, in spite of coincidental timing, that it has anything to do with RA or the drug. I'm giving you alternate possibilities as to what might be causing the stiff neck.
Are we on the same page now?
Having said that i do agree that it i likely something else altogether, and not related to MTX. Try a new pillow and/or ask your doctor to prescribe PT. PT helped my neck tremendously after a car accident.
Best advice, which we all gave - see your rheumatologist.
As for drugs, when you have failed, or had bad side effects for 10 or more RA drugs, that is the time to start worrying. Right now, the OP has a huge number of meds to choose from. And that is a very good thing!