の is a possession marker, similar to "of" in English. つもり is treated as a noun, so you need の between つもり and 学生.
(来年)日本に行くつもりの学生です/(来年)日本に行きたいと思っている学生です is grammatically correct, but this sentence doesn't work well for your situation since this refers to more likely "a student who are going to go to Japan (next year)". Your teacher already asked him to help you, right? Then I would say 私はこの前(your teacher's name)先生から連絡していただいた、日本に行きたいと思っている(your name)です。 (LIT.)"I'm (your name) who wants to go to Japan, whom (your teacher's name) asked you to help previously".