Have you combed your teeth today?
No, neither have I.
You can’t comb your teeth. So why do people talk of going over a thing with a (fine) toothcomb? They mean a fine-tooth (or fine-toothed) comb. That’s a comb with close-set teeth used especially for clearing parasites or foreign matter from the hair. Figuratively it refers to a detailed search or examination of something.
Perhaps the confusion arises because there is actually such a thing as a toothcomb.
Wikipedia tells us that “a toothcomb (also tooth comb or dental comb) is a dental structure found in some mammals, comprising a group of front teeth arranged in a manner that facilitates grooming, similar to a hair comb. The toothcomb occurs in lemuriform primates (which includes lemurs and lorisoids), tree shrews, colugos, hyraxes, and some African antelopes.”
Although many dictionaries allow “(fine) toothcomb” in the figurative sense of making a detailed examination, it’s nonsense. What people mean is “a fine-tooth comb”.
You can read about the correct use of fine-toothed comb and a whole lot more, in the Clifford & Co editorial style guide.