I'm having a really hard time visualizing what these looks like, and so my primary recommendation is going to be that you go to see your primary care doctor
! I think a doctor needs to take a look at this in person in order to get a better sense of what you are dealing with and help you figure it out.
There are many skin disorders that might affect the skin on the finger tips, leading to inflammation, peeling, or blistering. I suppose any of these conditions might alter the surface texture of the finger so that it looks like a small tentacle. For example, one of the more common causes of skin changes on the palm-side of the hands is a type of eczema
called dyshidrotic eczema, which can cause extensive peeling and small blisters in this area.
It also would be important to know if you have had any trauma to the area, such as from a burn or from cutting yourself. These factors could be important causes of the skin changes you are seeing, so make sure to mention this to your doctor.
Once your doctor examines you, I'm certain they will have some recommendations about whether you need to use any medications or other treatments to clear up this problem.