Hi. Thanks for a very elucidate history. The history of getting spam type of pain at the base of the tongue where the carotid is there and which is present only in the afternoon or early evening suggest that the muscles of this area really are going through the spasm, getting fatigued by the time afternoon or early evening comes due to may be continuous use of the throat or overuse of the muscles or added stress and anxiety and so on. I would advise you an ENT Examination by endoscopy to rule out any organic problems like a mass or ulcer and then give you a course of an anti-inflammatory medicines with muscle relaxant property and an anxiolytic medicines. Since all these medicines are prescription medicines, please consult your ENT Surgeon and get started properly.