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No. Shingles is a human virus that affects nerve endings. Cats cannot get it.
Most cats develop these symptoms as a response to allergies or fleas (or flea allergies).
I suggest that you get the cat started on frontline and then talk with your vet about an antihistamine and/or steroid to help with the itching and give the skin time to heal.
Let me know if you still have questions.
The frontline will not irritate the neck. It's normally pretty gentle.
Even if you don't see fleas, this might be the cause and that's why you need to treat it as that first. It only takes on flea bite to get it started when a pet is allergic to fleas.
Let me know if you have more specific questions.