Chapped Swollen Fingers from Sucking on Them.

I would rub lanolin on them and tuck them into some baby mittens while she sleeps to allow them to start healing.
During the day you can try to substitute the fingers with a teething ring, pacifier or toy. If it gets worse a trip to the Dr for more ideas and some ointment from the Dr might help too

Put some salve on them (to help them heal) and then make her wear gloves. Tell her no more sucking fingers. It's bad for you. Give her a "lovey" and tell her her special lovey will help her instead. This will be a process bc this is how she comforts herself just like a pacifier or thumb sucking. Good luck!

I'm not sure if you're looking for help on chapped skin (lots of creams out there - there's some creamy ones for eczema we use that don't rub off - just ask at the pharmacy, they come in a tube), or are you looking to have her stop the behavior? Is it new? Sometimes it is from teething. It might be pain in her mouth.

Put gloves on her hands, N..

Put a salve on them and then put gloves over them.

Talk with the pediatrician to see if there is something else going on. Does she have ulcers in her mouth? If so - she might have hand, foot and mouth disease. I would take her to the pediatrician.

Lanolin is a good idea.
Coconut oil is good too.
Try her on different teething rings.
Some you can cool in the fridge.
Some suggest a frozen waffle for them to gnaw on too.

Our son had a soft vibrating turtle toy.
You hit the back and the turtle would play a tune and vibrate.
He'd hit that thing and put it's head in his mouth and he liked the vibration on his gums.
The soft part was detachable and washable so we could keep it clean.