You won't cause extra damage by climbing the stairs but the pain will of course increase.
However, keeping a joint mobile is very important, as exercise aids circulation and reduces stiffness.
Rheumatoid arthritis most often affects the wrists, thumbs and fingers but sometimes the knees as in your case.
In natural medicine, the best remedy is Atrosan® (Devils Claw), which is licensed for rheumatic conditions and joint stiffness, on account of its anti-inflammatory action.
It doesn't interfere with any other medicines you might be taking and should begin to help within a month or so.
For more immediate relief, you might want to try Atrogel® (Arnica) before bed, upon rising and in the middle of the day.
It won't address the cause of the pain like the Atrosan® does but should help you feel more comfortable.
You may be feeling pain when lifting your arm because of some wear and tear in the upper spine, some tension in the shoulder and neck muscles or because of a condition nearly everyone develops, called scoliosis.
Please try to limit the tea and coffee you drink to no more than 3 cups in total and use the Atrosan® and Atrogel® for this situation too.