Could you be affected by 2 different types of eczema at the same time? say dyshidrotic eczema and atopic dermatitis?

Yes!: Your eczema may be of several types at the same time - it's all versions of the same process, all of which respond to similar topical medications. See your primary care provider for some good ointments that will help.

Yes: You could have your baseline atopic dermatitis and then get dishydrotic eczema from an untoward reaction.

Yes: Dyshidrotic eczema, sometimes called Pomphoylx is an itchy skin condition of the hands and feet, characterised by vesicles, fluid filled bubbles. It is distinct from Atopic Dermatitis however the conditions may certainly co-exist. Other conditions such as Irritant Contact Dermatitis, or Allergic Contact Dermatitis can cause itchy rash of (most commonly) the hands. See your Dr for history + exam.