M.H.
If you are home with her.. Sew a mitten into her pjs and have her wear them that way she can not take the mitten off. It will help to keep it clean.?
I have to say I did chuckle with the duct Tape response.
My mom had to do this when I had chicken pox, so I would not get them in my mouth and I was a thumb sucker.
Good luck.