Probably contact dermatitis.
New carpet is treated with some sort of chemicals to prevent staining. Carpet glue could also be the problem.
I'm sure you've washed your hands, but have you used that super dooper soap you use when you work on your cars? Have you changed out of the slacks you wore to work? You will have carpet fibers on them...new carpet "sheds" for quite some time...and if you rub your hands on your slacks, you are just getting whatever is making you itch, back on you.
After scrubbing your hands...if you have some hydrocortisone cream, rub it in to your hands real well. Take some benedryl if you have some. If you don't have either...go get some. Get the generic hydorcortisone...strongest strength..it will work almost as well as the brand stuff.