From the description, worse in the heat, better in cool dry weather, involving the left eye and the perfectionism I cannot see any relation to Arsenicum, in whatever form.
Among the kalis, only the hydriodicum and the sulphuricum are better from cool weather and the muriaticum is the only one with vomiting during the headache. I agree it may be Kali, but I would also consider one of the Natrum salts. Do you strive for perfectionism for yourself or to make a good impression on others?