missing fur after vaccinations

My cat is four years old and her name is QT. She developed Ashma back in May but is doing much better with that. However, this past Sunday we went to the vet to get our yearly vaccinations. The guy who gave her the shot put them all in her neck area (which i thought was weird because they usually give them to her in her butt), anyways, monday morning I woke up and she had a patch of fur missing right around the area where the guy gave her shots. She has had these shots every year since she has been born so I know she can't have an allergic reaction to them. I called the vet and they told me that the shots probably irritated her skin and she did it to herself. Now she wont leave it alone so she has been wearing a head cone collar for the past day and a half. How long do you think I should make her wear the head collar? I feel so bad for my little girl she so sweet and I feel bad making her wear the head collar she is so depressed.

I'd leave the e-collar on her whenever you aren't able to watch her as long as she is still trying to scratch the area. I would also be concerned about why she was given shots in the neck area rather than the hindquarters. If your vet doesn't have a good explanation, I would consider switching vets. Vaccine associated sarcomas are pretty uncommon, but they can be very serious. One of the main treatments is amputation, but that can only be done if the vaccine is given in the leg.

It is not true that it can't be an allergy because she's had them before and had no problems.
The first exposure is usually safe (exceptions being a cross-allergy). It's the second, third or later time that you have to be concerned. So it could be an allergic reaction.
I'd talk to the vet.