Can I ask how old you are? When I was developing my breasts itched and hurt and felt raw sometimes from about 11-13 until I was done.
When you press down, do you feel any kind of abnormality there like a lump or cyst? By itch do you mean a tingling or an itch like a bug bite? An itch like a tingling feeling or a numbness I would definitely have checked out because that can indicate something neurological. Have you been keeping track of what you are doing before or during these "episodes"? Or have you noticed anything that triggers it? Those things can be very important if it is something that requires a doctor's visit.
Hope everything turns out okay! Keep us updated!