Rheumatism is the umbrella term for any disease of the joints. The particular type of rheumatism that affects the hands is often Rheumatoid Arthritis. Around 20% of people with a form of rheumatism will have this one.
Unlike wear and tear arthritis (Osteoarthritis, which can also affect the hands), Rheumatoid Arthritis sees your own immune system attacking the joints, hence the swelling, heat and pain.
The trigger for this is unclear, although abnormal bowel bacteria have been proposed as a cause as have very bad levels of stress, chronic low level inflammation, long term Omega 3 deficiency and genetics.
Make sure your intake of oily fish or linseed is good (3x a week), your intake of dietary fibre is high (preferably from colourful veg for the antioxidants) and please consider our Atrosan Devils Claw tablets as they are licensed for Rheumatism in general.
Your Doctor can confirm what it is via blood test but if both hands are affected, it suggests Rheumatoid Arthritis to me as wear and tear tends to affect joint unevenly.