Occasionally I warn about using the wrong case for compound objects of prepositions (between him and I is wrong, him and me is correct). So Ordinary Bill has a little test for you. Warning: it’s tricky. Look at the last panel:
Was she correct to say “my boyfriend and I”? Should she have said “my boyfriend and me”? Why or why not?
Well, she’s correct! We don’t have a preposition here, so it’s not a compound object. We don’t exactly have a verb, either. We do have an implied verb, taken from what the garbage man says. Her implied verb is “is.” Ah, so compound direct object, right? Nope! Linking verbs (any form of “to be” in this case) take predicate nominatives. The linking verb is equivalent to an equals sign, so both ends of the sentence are equal, hence both are nominative. Her full statement is something like, “Nope, it is just my boyfriend and I.” Maybe she’s saying “Just my boyfriend and I create this mess.” (That would make it a compound subject, which is a little easier to deal with.)
(Yes, saying “the English teacher is I” is correct, even though it sounds bad. Instead, say, “I am the English teacher.”