M.Y.
I was a nailbiter when I was young but I think this home remedy that my grandmother used when I stayed with her one summer should work for finger sucking as well and it doesn't involve peppers. You will need to two things. A can of alum powder and a washcloth. Alum powder is on the spice aisle at the grocery store. It is used for canning or pickling.
My grandmother would keep it on my fingernails and if I put them in my mouth it was like sucking on 10 lemons at once. It doesn't really have a flavor per se but it is VERY tart and yucky! She would keep a damp washcloth with her whenever we went anywhere. If I put my fingers in my mouth I had to keep the washcloth in my mouth in place of it and in public!! It only took a couple of days and I never did it again.!! Good Luck!