maybe lymphangitis but what do i know. . . see http://www.telemedicine.org/3assess.htm
My son had this, check in the mouth for ulcers. He was diagnosed with hand foot and mouth disease. And I thought only cows got that!!! It is a virus and should clear up on its own. I think!
I'm afraid I can't say a great deal from here. It sounds like an unusual case. Eczema can cause blisters on the hands and feet, but that wouldn't explain the soreness, or the swelling and red streaks (unless that was a separate matter, perhaps a bacterial infection on top of the eczema.) It may be that time will clarify the matter. Sorry I can't add much.
Best.
Dr. Rockoff