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Clothing & Shoes: Place garment in the freezer for several hours then peel off the bits. Cover with a piece of wax paper then run a warm iron over top, the remainder should melt into this paper. You could also try pouring boiling vinegar over top to help it dissolve (this is a tried-and-true for gum that had been washed and dried in the laundry).
How To Remove Gel Nail Polish, At Home! another tip - at the salon they heat the nail varnish remover. They also use a very fine filing board to polish the nail to a healthy sheen, which might have been scraped before the gel was applied.