"The Advocate, the holy Spirit that the Father will send in my name--he will teach you everything and remind you of all that I told you"
You are correct...but it is not your "interpretation", it is your understanding of the verse and passage (which is the same as I understand it).
I say this because what Jesus promised was given strictly to the Apostles. In this respect, your explanation (what you call your interpretation?) is a comment on what Jesus said. Can you understand that?
God did not give special privilege to the Apostles, only special burdens. I know it is contemporarily popular to play theological "gotcha" by citing this disclaimer, but that contradicts what else is said slightly further on in John:
John 14:21 Whoever has my commandments and observes them is the one who loves me. And whoever loves me will be loved by my Father, and I will love him and reveal myself to him."