It does sound psychosomatic to me. Don't get me wrong, I'm not denying your experiences at all, I really do believe that you experience the itching.

I'm also fairly sure that the doctor would have suggested an allergy test if she thought it was to do with alergies. Instead... She suggested it may be psychosomatic.

Did she say what she thought you should do about psychosomatic itching? Are you seeing a therapist at all?

What leads me to think it isn't an allergy is...

In particular...

The part about how you: 'immediately have itching in [your] mouth, throat, ears'.

Ears is a strange one. Especially the 'immediately' idea...