Use fawning to describe someone who's over the top in the flattery department. Like a fawning admirer who just won't stop complimenting your looks, showering you with gifts and otherwise kissing the ground you walk on.
From the Old English fægnian, meaning “rejoice, exult, be glad,” fawning can be both an adjective and a noun form of the verb fawn. Fawning people are often trying to win favor with the person being flattered, and it sometimes comes off as sucking up. So do everyone a favor and don't try to boost your poor grades by fawning over your professor’s every word.