Whenever I shovel my driveway, I come inside, and my hands get all red, swollen, and itchy and irritated.
Like all the blood is rushing to them, or something.
So I hold them up above my head and put lotion on them (because it feels really good to rub lotion on them when they're like this.)

So...
wtf?
and does anyone else ever get this?

you are having an allergic reaction to something. It is possible that it is a reaction to the cold.

I cant wear scarves at all. My skin cant handle the heat locked in around my neck contrasted to the cold blasting me on the outside of it. I would get these horrible looking blistery bumps on my neck that would itch like hell whenever i worse a scarf in the freezing cold. I went to my dermatologist and to put it into the simplest terms, he said my skin gets confused by the drastic changes in temperature and doesnt know how to react. There is a medical term for it but i cant remember.

Maybe you get the same thing on your hands. Do you wear gloves when you shovel? If so, your hands are getting all sweaty underneath the gloves while the cold is pressing on the outside of the gloves. It sounds like you are having a reaction to the temperature. Lots of people have skin reactions to temperature. My friend gets bad, itchy, red welts on her face from the cold. I get itchy hives when it is too hot etc....

My bf got something on his knuckles that sounds similar to what you have. he was rubbing excessive amounts of lotion on his hands because it made the bumps stop hurting. I gave him some of this medicated lotion from my dermatologist to put on his hands and that helped.

Frost bite. ("frostnip" is the 1st degree term.)