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Sorry this is late.  Been very busy.  I still do not know what is causing the itch but have made sure that any dye I use is gluten free.  I used Loreal Superior Preference.   Rinsing my hair after washing with diluted apple cider vinegar really helps.  I also stopped eating oats about a month ago.
The itch is still there.  I even have small bumps on my scalp now.  It is annoying but not terrible.  Seems to come and go.
Thank you to all that replied.

The replies I got were to use:
Essential Oils
Steroid Solution
2 said they take Benadryl right before dyeing 
Tea tree shampoo
Hydrocortisone 1% cream
Aveda soap rinse
A few wondered if it is Psoriasis.  It is not really red so I am not sure.

You can just do a general search on gluten free hair dye and you will get a list.

Ginny Mingolla

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