Liquid nitrogen wart removal

Hopefully someone here has experience with this. My daughter has a large wart on her index finger of her dominant hand. Her dr wanted to freeze it off since she’s had it for a long time and nothing is getting rid of it. My daughter is almost 5. She sat well while the dr sprayed it. And I noticed some of the spray went down her hand. Now her finger is swollen, blistered..she was miserable afterwards!! Idk what to do, if this is normal or not..my husband is furious, I’m beating myself up for giving the ok to do it. Help! She’s currently sleeping, but you can tell it definitely hurts while she’s awake. She refuses to move it and is really babying it.