i would not freak out over it. don't show her any stress you feel.
do get a quality, regular hand lotion, such as vaseline intensive care, get a pump bottle and put it right next to the sink where she washes hands. do this in a fun way, not a stress problem. set up the hand washing area so that she first uses soap, then uses a nice clean towel, then when her hands are try, she gets some nice lotion to rub into her skin, especially the skin around her nails. you can rub it right into the nails, and the surrounding skin. don't gob on so much that it's overwhelming. just a little shot on each hand, and rub thoroughly. this will lessen the amount of dry skin available to trigger her picking habit. keep her hands moisturized and supple.
then, when this is the new "normal" for her skin, you can see if she moves on to another thing to "pick" -- in which case she might be a "picker." or maybe she can move on to something else altogether.
are you giving her good tactile outlets? those touch balls with the long spiky soft tentacles such as you can buy at the dollar tree are good. point out opportunities to touch stuff. give her touch outlets. she may just be really into touch.
i would avoid psychological help for this, if you can instead redirect her to touching something more appropriate.
having dry skin around her nails is a situation you can control if you are diligent about using the good quality lotion. also make sure she always dries her hands thoroughly after washing them. i say take care to provide soft, FRESH drying towels. if she's "into touch," these kinds of "small" considerations are noticed and greatly appreciated.
i say all of this as someone who is also concerned with touch. my son is a "toucher," always has been. when he was a little baby he wanted so badly to twiddle the opposite nipple while he nursed. i could not stand that and never allowed it, but he moved on to my armpits, and now finds comfort and security touching the stubble while he nurses. LOL it's cute and doesn't hurt anyone. i just gave up on deodorant for awhile so he doesn't' touch chemicals.
i always point out opportunities for him to touch stuff (when it's appropriate) when we are out and about. like, "ooh, i bet that feels neat. want to touch it? go ahead..." he went through a faze in which he bit his nails. but when he went to far and made them bleed, i stayed calm and explained why that happened, and that this is the risk you take when you start biting your nails and fingertips. i let him own the responsibility for it, but i also stepped up by diligence about using the lotion. when a child is asleep at night, you can also "do" their hands with lotion to soften their skin overnight. a quality lotion will get rid of "rough" skin or sharp points around the fingernails. you can solve this particular problem quickly.