My wife has puffiness under her eye like she got punched in the eye and she is itching in her hands and feet as lot.?

Allergy response. It sounds like she has allergic reaction. The puffiness around the eye and itch else where most likely reaction to some allergen. Take some kind allergy Med like Zyrgan or Claritin (loratadine) may help with her symptoms. She can wash her closed eye with cold water or ice it. If it's still persist after a few days then she needs to visit a doctor.