Yeah its not muscular pain, its nerve involvement.. Since you are having this throbing pain from a week better take physiotherapy treatment.. Nerve stretchings will help you.. The more time to take to get it treated it will take more time to heal.. So better take Physio sittings...
Next Steps
cooking is your job... for the time being you can take precaution, use your right hand more while cooking... avoid heavy exertion from left hand..