I think it will be very difficult to trace down to whether there is a crest or coat of arms.
There are several variants on the name spelling -- you use the same that my father and his father used -- Jimerson. However there are also those (and I'm not sure whether they are related) who use the variant Jimmerson. Then granddaddy Jimerson's own brothers in several instances spelled it Jamison. (I think that reflected much of the pronunciation of the region.)
It all boils down to possibly be lines deriving from one "James" -- hence Jamerson, Jameson, Jamison, Jimerson, etc. Some say that it's a Scottish line coming from "Hamish," a variant for James. (I can't vouch for that at all.)
Darwin, do you know any more about who your father's parents and grandparents were? Beyond my great-grandparents is where I'm running up against a blank wall. I can't even find all the married names of Granddaddy's sisters.