as you may realize i have not way of seeing those "white spots" by an examination and your description is just too vague to make any type of guess as to their nature. some white spots are simply trapped food particles (the tonsils have little holes and crypts) and some can even calcify (tonsilliths). antibiotics are not really necessary if your strep test (and a follow up culture) are negative for pathogenic bacteria. viral infections of the throat will resolve in about a week and can also cause "white spots".
white spots on tonsil on right side but strep test was negative? also swollen lymph gland in neck on same side. . what are the white spots on the tonsil if not an infection that should be treated with an antibiotic?