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Arthritis of the hands most commonly presents with swelling of the hand joints, painful movements, redness and reduced mobility of flexibility of the joints.
The most common cause of arthritis in the small joints of the body can be rheumatoid arthritis or osteoarthritis. Other conditions like psoriasis, infective arthritis, gout, inflammatory conditions of the soft tissues (Synovitis, Flexor tendinitis, etc) can also be the cause of your symptoms.
For the time being, you can find relief by taking anti inflammatory medications like Advil, motrin, etc, which will reduce the swelling and the pain.
Other measures that may help include
1. Alternate hot and warm compresses
2. You can soak your hands in warm water and salt for about 15 to 20 minutes. You will have to repeat this at least 2 to 3 times a day for best results.
But for proper diagnosis and definitive treatment of the condition, you might consult with your doctor for a complete physical examination and investigations including Xrays and blood tests (RF, CRP, anti CCP antibody, etc). Treatment will be based on the specific cause.