Scared for 3 1/2-year-old toddler who says she can't stop picking...says she itches?

My 3 1/2-year-old is very verbal. In fact, her speech is far more advanced than her emotions. I believe she may have high anxiety. Things set her off into screaming tantrums...for example, if I pick up the dog's leash, this can trigger her to jump up, start crying and race around the house looking for shoes. She is afraid she will miss out on taking the dog out. We went to the mall with friends and if they walked to close to the door of the store, my daughter would begin jumping, pulling away from me, whining, breathing hard, then finally cry, saying "they are leaving...they are leaving." I have not taken her to anyone yet for any type of diagnosis...this anxiety is just becoming clear to me. Now, to the picking issue. From the first day I brought her home, she would reach up, grab her hair and pull...then scream and cry. After repeatedly removing her hands from her hair, this habit was broken. Then, I was not the best at keeping her nails cut short and at about 6 or 9 months, she scratched the top of her nose while sleeping. After discovering the "spot" on her nose, I would have to take away her hand from it constantly. through the first 1 1/2 of life, she commonly had this nose spot. It would heal, she would scratch it again while sleeping, then I would have to "watch her" while it healed. The summer she was two, she experienced mosquito bites. At first we were fine, but then she figured out she could scratch them. If I found them, covered them with band-aid, they would heal. This summer, when she was 3, was hell on me (and it is still going). She will pick any sore (mosquito bites, scraped knees, etc.) and will pick them deep! I have tried explaining she is hurting herself, I covered them with band-aids (but she removes the band-aids), I dress her in tight fitting PJ's at night so she can't pull up legs and arms and pick, I have even lost my cool and spanked! She tells me they itch, she can't stop, she does not know why she does it...she's 3 though so how could she know exactly why? I will find her sitting on the potty (she takes herself now) picking her leg sores and bleeding. she immediately says "sorry mommy" and tries to hide what she has picked. I clean her up, cover it with neosporin and band-aid and remind her not to do it. She has sad puppy dog eyes. I tell her, please come to me and I'll help. it is better to come to me, than hide. I decided 3 weeks ago to put a pair of socks on her hands. Better than gloves because she does not have use of her fingers. the rule is she wears them if I see her pick or try to pick. I know this is helping because...she has a sore on top of her left hand and her right hand lifted up to pick it and she stopped herself and put her hand down. I guess what I'm asking you guys is a couple of things... 1. Does anyone know if they had these types of behaviors this early?? 2. My daughter had eczema when 1 and 2, but it seemed to go away when I changed family diet to gluten-free. We are back to eating normal bread and pasta (full of gluten) and I'm wondering if the "itch" she says she feels is actually eczema? I don't know if she is too little to feel the psychological itch to pick?? Does anyone else now of a link to eczema or had improvement with change of diet (i.e. gluten-free diet)? 3. Did I cause this problem?? I was diagnosed with depression when my daughter was 5 or 6 months of age...it was not postpartum depression...she was the best part of my life...the problem was not having my husband around to help. I felt scared and alone, and I became depressed that my husband was not enjoying this time in our lives as I was. There were times when I cried quite a bit through the day. I wonder if my depression and anxiety "taught her" during this critical time of emotional development. Is my daughter punishing herself this young because of sad feelings? Is she doing this because I spanked her and now she feels she needs to punish herself in some way? As a teenager, I experienced anxiety to the point of not making friends in school...but I never ever hurt myself. I did not know I had anxiety as a teenager...I was just "shy" but in college psychology class it became clear. I'm a real self-help type of person and immediately began working on my social skills and feel I've made huge improvements! It's amazing too...being a mom really makes you brave and strong. You got to be for them. Also, my husband says he picked his sores like crazy when he was young. Says it drove his mom nuts! He has an addictive personality. (This scares me.) My mom told me I have an aunt that picked her scabs like crazy...has scars on her legs...she also is a highly addictive personality with drug problems! (This scares me.) I'd like to hear what anybody has to say... Thanks