Can something like wearing a hat all the time cause a neuralgia in the forehead or irritation that would cause a numb sensation?

Low likelihood: While theoretically it is possible that very tight hat over forehead may compress sensory nerves of forehead and cause numbness but in reality it will be extremely rare.

Very unexpected: Not clear what you mean by "neuralgia in forehead", as am not aware of such an entity. Not clear where the "area of numbness" is located. Perhaps best way to sort this out is to go to our paid website to have a more thorough virtual consult.