From your description it appears that you have lymphangitis
since there is redness
, warmth and pain. It is most commonly caused by infection in the distal part of the limb which is the hand so search for a source carefully there. The lymph vessels drain upwards that is why you have the red blotchy line going up to your elbow. I would ask you to consult a surgeon on an immediate basis to discern the cause of the infection and you would possibly require antibiotic therapy and analgesics.