I don't think neighbour and friends are the same, like in English(well you can be a friend with your neighbour :) ). Your teacher is not wrong but that might be a bit too long...(Japanese people tend to say things as short as they can)
If you say "a new friend" in Japanese, it would become; 新しい友達
If it's a new neighbour, you would say; 新しいご近所さん or 新しく近所になった人
I hope this would help :)