Could someone possibly eat too many cough drops?

That depends: What type they are? Some are medicated & some are not. Try this: hydrate well. Consider using a warm air vaporizer. Mix several teaspoons of honey into herbal tea with a squeeze of lemon juice. Or make tea with 2 tsp of marshmallow root bark per 1cup of hot water (steep in a covered pot for at least 5 minutes). Drink several times a day or as needed to relieve coughing. See a physician if >.