Occasionally my 18 month old will have a really long cuticle on one nail, the skin around the nail peels and the skin underneath is wrinkled. why?

Maybe not a problem: Sometimes kids have little tags or bits of skin that stick out next to fingernails. Sometimes it's a little hangnail on the side of a nail. These can be safely snipped of by the doctor (or parent, if he/she has good eyes and steady hands) with tiny scissors like the ones on the smallest swiss army knife. I am not sure why these things happen, but they just might be a part of life.