She keeps picking at it because it's beginning to itch. I would have still continued to keep neosporin on it. Since it is itching, it is still in the healing process. Neosporin is also wonderful for reducing scars. It's better to keep it open now, and band-aids are only needed for the original few days, when it's still in the bleeding process.
Don't use that "second skin" bandaid stuff. It'll burn. That's for small cuts & scrapes, not for face injuries.
I also wouldn't use ear piercing solution on anywhere but the ears! We actually use Band-Aid's Hurt-Free Antiseptic wash - it's in a blue bottle. It's only a couple bucks, I think I found it either at Walmart or Walgreens. We buy it in abundance in this house! It doesn't sting, and it streams out just like the hospital does, when they do an antiseptic wash. I use cotton balls & Q-tips to help get dirt out. Otherwise, if there's no dirt in it, just lightly wash her face with water when you give her a bath. Put neosporin on again, when she's sleeping so she won't wipe it off.
I use this sequence, not only because I don't like to see my children in pain, but also - I don't want them to scar.
Mom of 5 children, now awaiting birth of twins.