Hi, this is Dr Sathya. Thanks for your question and I am very glad to help you.
Yes pinched spinal nerves can cause uncontrollable itching of the skin. This is a very rare complication of pinched spinal nerves, but can occur.
In fact there is a condition called as "Notalgia paresthetica" and this condition is thought to result from pinching or irritation of the spinal nerves.
If your family dr & skin dr do not suspect any other possibilities to explain the itching then your bothersome itching may be attributed to pinched spinal nerves.
The treatment options for this condition include;
Antihistaminics like Atarax (you have used already)
Local anesthetic creams or patches like Lidoderm skin creams or Lidoderm skin patches
Topical steroid creams
Topical Capsaicin skin creams
If the above measures do not help then one of the following may help;
Paravertebral nerve blocks
Surgical treatments to relieve the pinching of the spinal nerves (as a last measure if nothing else helps)
You may go through the following article to gather more details in this regard;
Please ask me if there are any further questions.
Thanks for the waiting!
All the best!
If you have any additional questions, concerns or clarifications then please let me know. And if you are satisfied with my answer please accept it so that I will be credited for my expertise, time and effort put in preparing this answer.