Is it possible to be allergic to mosquito bites only on certain parts of the body?

While outside in my pool last night, I got two mosquito bites. One on my neck, and one on my back. The one on my back puffed up about the size of a quarter, was red on the outside and white in the middle. The one on my neck was like any old mosquito bite. Also, the one on my back itched instantly, whereas the one on my neck has yet to bother me.

Unless it wasn’t a mosquito that bit my back… I’m just assuming it was.