The technical term for the pins and needles feeling you get when part of your body "falls asleep" is 'paresthesia'.
This word comes from the base words ‘para’, which means “altered” or “abnormal”, and ‘aisthesis’, meaning “perception”. Most people are familiar with this sensation - it commonly occurs when a person has slept on their arm or left their legs crossed for too long. The feeling is caused by sustained pressure on a nerve. Paresthesia is typically fleeting, but if it lasts a long time or occurs frequently a medical condition is likely to blame. Chronic paresthesia can be caused by a neurological disease or traumatic nerve damage.