X-rays are unable to detect any early
changes of
osteoarthritis. The pain starts years before appreciable
changes can be detected through X-rays. A repetitive tendon injury is a likely diagnosis. Also, it could be osteoarthritis since you have pain in both thumbs. Another possibility is rheumatoid arthritis. Both can cause symmetrical joint involvement.
The treatment is rest, physiotherapy, occupational therapy, and non-steroidal anti-inflammatory such as Tylenol, Aleve or Mobic. Take care!