Firstly, "내일 학교에 갈 거예요" is the correct sentence. Secondly, 에요 is actually supposed to be written as 이에요. Both of these are semi-polite versions of, 이다. 이다 means "I am, they are, it is, etc." The difference between the two are when you're supposed to use them. 이에요 is supposed to follow something ending in a consonant. Like in the sentence, "저는(I) 미국(american) 사람(person)이에요(am). 사람 ends with a ㅁ, which is a consonant. That's why it uses 이에요.
예요 follows after words that end in a vowel, like in the sentence, "저는(I) 여자(woman)예요(am)." 여자 ends with ㅏ, which is a vowel. That is why it uses 예요. :]