The skin on some fingers and thumb of my left hand is peeling since a long time. I live in Arizona (dry weather) but I don't have sunburns.

Atopic dermatitis. Lichenification (dry, cracking, possibly leathery, hardened, peeling skin) is a common consequence of atopic dermatitis (eczema) and other pruritic (itchy) disorders. It may also arise on seemingly normal skin. Get an eval for your diagnosis and any treatments needed. Good luck.

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My right hand fingers (middle, index) skin are always peeling and dry. It doesn't hurt or anything just sometimes itchy. It's been like this for months. A few days ago I start to notic my thumb tip skin is also peeling and now it left a blister on my t?

Dyshidrotic eczema. Without seeing it you probably have chronic hand eczema. A very common skin problem associated with chronic exposure to certain soaps or other substances or with frequent hand-washing,just to name a few. If you can identify something like that avoid it or use gloves during exposure. Barrier creams can help retain moisture. The treatment of choice is high potency steroids; you may need a script. Read more...

I noticed since last week, my left hand skin has been peeling right after washing it; mainly between the fingers and palm area?

Needs... It sounds like you might be having a dermatitis or in other words an inflammation of the skin which could be reacting to an external agent, lack of moisture, or any physical condition that could trigger it. However, a final diagnosis of a skin condition can only be attained by direct visual exam. My advise is to see a medical provider for diagnosis and treatment. Read more...