Where should I be after 3 months playing is a loaded question. Ask yourself the following questions:
1. Why do I want to play guitar?
2. At what level?
3. How far do I want to take it?
Answers:
1. Because I love guitar!
2. As far as I can push myself!
3. Thats up to you!
In your post you don't say if you're learning songs? If your teacher is showing you what you want to learn that's great; theory is worthless unless you're making or re-producing music you love.
Find 5 songs you love and ask your teacher to work through them. The chord progression, the melody, the harmony, the feel, the tempo; in other words, analyse the songs. Work on them 1 bar at a time if need be but always, always play what you love, build a repertoire.
As for theory it has its place depending what you mean by theory. If you want to be a session player then you need to have a good ear, a good understanding of harmony, the ability to sight read standard notation, and the ability to play what's required in 1 or 2 takes. If you want to play your own stuff get creative; learn some basic patterns and experiment, don't close your mind to anything and stay hungry. Get hold of some good quality tabs/music score and learn what you love. Ask your teacher to work through some songs you want to learn in whatever genre you're into.
Music has so many variables; the bottom line is decide what you want from music and go for it 110%.
Yours in music
UOTRaxeman.
