Does hydroxyzine HCl 25 mg stop exzema from itching?

It can, but... Medicines like Hydroxyzine and Diphenhydramine (benadryl) can help with itching associated with eczema. However, the best way to get relief is to treat the eczema itself using topical medicines, ranging from over the counter euceryn to prescription drugs. Hopefully your doc can help, and they aren't, see a dermatologist if you can.
Will help. Hydroxyzine is an old antihistamine that relieves itching. It will help, but it has a common side effect of drowsiness and impaired reaction time, so a person who takes this must be careful when "driving and operating heavy equipment." other antihistamines with less drowsy side effects will also help with itching. Skin care is the initial approach to treating eczema.