Thanks for your query.
From the description, I feel that you might have sustained a SOFT TISSUE
STRAIN involving your ligaments or tendons.
Since the pain is persistent for 4-5 weeks it needs to be investigated. MRI
scan is the investigation of choice to detect any such soft tissue abnormalities.
In the meanwhile, for symptomatic relief:
1. Give enough rest to your hand and arm muscle.
2. Take mild pain killers like acetaminophen
3. Stronger prescription NSAIDS with muscle relaxants may help if simple analgesics do not help.
4. Hot compresses to your arm will be useful pain relieving measure. You may apply a local analgesic gel on that area.
I do hope that you have found something helpful and I will be glad to answer any further query.