I cannot remember an American lamp in pottery when I was doing shows and buying at flea markets but it has been years since I was an active dealer.
Here is an idea: find a small bulb, e.g., a Christmas tree light bulb, to insert (after taking the burner out) and see if the glow shows through or not.
If it does, it is probably glass.
Is the lamp painted? I cannot help with the burner, Skipinphx :})