There is a type of itching called "brachioradial itching". In this case, the hands itch from the wrist to the elbow. It is believed that this may be due to nerve fibers. This itch is more common in middle-aged people with fair skin. It gets worse in summer and especially in hot climates. To test this itch there is an ice test. You need to put an ice pack on the most itchy place for 15 to 20 minutes. If it has become noticeably easier, then this is it. This is what a neurologist does.
This itch can be neurological in nature, it can be of an allergic nature. To understand the exact cause, an examination by a dermatologist and a neurologist is needed.