styes and two year old

My daughter has a habit of sucking her thumb and playing with her eyelashes
all at the same time . This causes her to get stys quite often. We have been
treating them with antibiotic ointment, warm compress, and we try to keep
her nails cut short.This usually works and they go away quickly. She has
developed a sty now that has lasted over a month. we can not get it to go
away. Her pediatrician wants to drain and scrape this one. I don't know how
I feel about this because it would mean staying at the hospital and being
put under anesthesia. I also feel until we get her to stop sucking her thumb
that this will be a on going problem. I'm looking for others thought on
positive ways to get her to stop sucking her thumb!