Final answer:
The nerve accidentally impaled on the needle was the median nerve, which caused the patient to experience pain and burning in the middle and thumb side of the palm.
Step-by-step explanation:
The nerve that was accidentally impaled on the needle was the median nerve. The median nerve is a major nerve in the upper limb that supplies sensation to the middle and thumb side of the palm. When the needle pierced the median nerve, it caused the patient to experience pain and burning in that area.