My guitar teacher says my guitar has intonation problems, so after tuning it this afternoon, I checked it out.

The low E has a tiny difference between open and 12th fret, like 20 degrees on my tuner (which has like, a 90 degree flat, and 90 degree sharp), and the B is similar. The guitar goes out of tune quite often as well.

Funds are a bit tight, so I would rather avoid getting a setup, but do you guys think it is necessary?
Save your money and do it yourself. In the process, you'll learn how to work on your own guitar. As already asked, what kind of guitar is it and what type of bridge does it have?
Tis a Schecter Omen 6. I think the bridge is fixed... there's no vibrato, but there are individual saddles, I know that much... I think :P

I'm just really terrified of turning the truss rod too far and snapping the neck, ruining my only axe :/
you don't need to touch the truss rod to fix intonation problems. i don't know your Schecter guitar, but there should be something on the bridge so that you can make small adjustments to each string individually effectively changing the length. its usually a small allen key socket.
I've been imitated so well I've heard people copy my mistakes.
- Jimi Hendrix
There should be an alun key socket or a screwdriver adjustment bit...tuneomatic bridge i think, but I don't know how those work, never had one. Sorry!