You said she's doing this while waiting for food and before naptime. Is this her way of comforting herself?
My youngest was much smaller than her older siblings at birth (by more than two pounds) and shows me she's ready for nap/bed by chewing/suckling on her index and middle finger. For a while, she did this so excessively that she'd gag herself and vomit (I found out it was due to teething and she was trying to ease her pain).
She continued this even after her molars were in, so I let her start taking a small stuffed toy to bed. I know there is a LOT of controversy over when to let a child sleep with a blanket, stuffed toy, or pillow, but I found she was ok with a small (6-9 inches in height, and no fluffy padding) bear during nap time and then extended it to over-night. She loves to cuddle, and with Bear she doesn't need to chew on her hands. She's no longer suckling so much, and she's actually gaining weight and seems MUCH more rested in the morning.
Talk with your doctor to be 100% sure. I'm not a fan of pacifiers, but in my opinion, it's better than sucking a thumb or biting your nails (27-year nail-biter here..). Pacifiers can be taken away eventually and can honestly give comfort. That would be a last resort in my eyes, but whatever you can do for your little girl is worth it. I hope you find something that works for the two of you. :)