Frankly, I wouldn't do it. It may be effective for a time, but often dosages have to be increased over time to remain effective, and it's very hard on the body.
Look into the natural supplement Quercetin, it's a natural anti-histamine and may very well help alleviate the itching. You'd have to give it on a daily basis for some time to build up efficacy though. The big thing Quercetin has going for it is that it is 100% natural and harmless.
Alternatively you can try benadryl on an as-needed basis. 1-2 mg per pound of body weight up to 4 times a day. The dye free caplets are good, or you can use the liquid version made for kids.
Thanks Mordy, and thanks to everyone else. I will take your advice and not have the vet administer the shot.
In regards to the diet questions...
My beagle gets:
1 cup of Blue Buffalo with salmon oil and a natural powder mixture containing bone meal, nutritional yeast, lethicin, and kelp.
At night, I usually give her something like a frozen chicken wing.
And for treats during the day, I usually use organic yogurt in one of her kongs and some freeze-dried liver.
Her diet hasn't changed since I rescued her. She started to scratch as soon as the weather got hot.
As an aside, should I still take her to the vet? I have an appointment on Thursday. I'm not letting them give her a shot, but would it be worth it just so her skin can be looked at?