I have a problem with my thumbs (and sometimes fingers) in that the ends split all the time - and it is jolly painful, especially with all this handwashing. The only way to help them heal is to cover them, but no plasters will stick beyond one handwashing.
Have you tried the Hydrocolloid ones? They are clear plastic and softer than usual ones. Boots sell them in different sizes and shapes. I find they stick well but not sure how good they’d be on fingers. Good luck. .