I voted for @Chrys' comforting and beautifully respectful answer, but wanted to add an idea to what Chrys had to suggest. During periods of change, kids often just need to know that something is staying the same. For your daughter, maybe the thing she needs to cling to right now for "sameness" is that she can have a hand to hold while she falls asleep.
Babies change things - it is part of the deal, and learning how to cope with those changes is a good thing for kids. However, it probably goes without saying that keeping as much of her routine as similar to the way it used to be as you possibly can for now may be a tremendous help. I recommend that for a start, plus, let her have your finger to hold for a little while.
As you do decide to wean her away from this particular comfort object though, show her how she can even hold her own finger when you aren't there. It will have a similar (albeit, smaller) feel to your own. She may even learn to grab for her own hand in the middle of the night without really realizing what she is doing and be able to self-sooth again as a result. Start by having her hold your finger and her own. Then remove your finger but sit with her and rub her back or forehead a little while she drifts off, then spend a few nights just sitting with her (while she holds her own finger), and so on until you no longer need to be in the room at all.