Wrinkled nails usually reflect inflammation of the skin at the base of the nail. If you have eczema or redness there (or if you pick at it), that would explain things. Fungus does not generally cause involvement of one nail on one
handHand or foot spasms
Hand tremor.
I can't think of any relationship between this and the itch points on your palm (probably a mild form of eczema) or the pimples on the body (most likely folliculitis.)
Except for the moisturizing you're already doing, I can't think of anything else worthwhile for the palms.
For specific diagnosis of the nail, I recommend a visit to a dermatologist. One visit should suffice.
Best.
Dr. Rockoff