If I have cold sores on my mouth can they spread further down into my throat?

Unusually at 33. Herpes simplex is usual cause of cold sores. By the 20's & 30's most have some immunity & sores stay localized. If. This is first time, called primary herpetic stomatitis then it can spread. Also suppression of immunity from drugs or disease can allow spread. See your dentist or physician for medication. Laser dentists can accelerate the healing process, especially with biolase waterlase or ezlase.
Easy to treat. Go to a health store and ask for lysine. This is an Amino Acid and taking a regular dose prevents cold sores.