Is it normal that i often think about eating my fingers?

Not quite the same but I like my nails and have been eating them since I was a child in recent years I like biting them to the quick causing pain which can be uncomfortable: I guess that is not the same as your fetish.

It's definitely not something that is on the average person's mind as often as it sounds like it is on yours. I think you enjoy licking your hands from the salt deposits that lie on your skin, but it's also a bad way to catch a cold that you could've avoided just from refraining licking your hand to begin with.

You're probably developing dermatophagia. Google it and even if it doesn't seem to fit your situation, you should go see a psychologist about this.

Someone said in the posts about eating hands that this is a psychological condition. You should see a therapist.