There must be something wrong with my AP English/British Lit. class. According to this class the first English language poet was Caedmon

Sorry, I am no scholar, so I am unable to help. However, from a purely lay point of view, for a teacher or reference work to say "the first English poet was ..." seems a bit ambitious. For the statement to have meaning, one must accept a definition of "English" and "poet" - and then prove that no one matched that description prior to the chosen individual. As it happens, my book attributes Cuckoo Song to that most prolific of authors - Anon.