Firstly, gotta say, good on you for seeing someone about it!! And even better, good on you for seeking advice! I can't imagine it being easy telling a bunch of strangers about this particular issue, even in such a "private" place.
If you have a proper psych report, I reckon you'll qualify for SEAS. If not, you don't really lose anything by not applying - the worst thing that VTAC can do is not give you benefit. Particularly if you're going to see your psych again later in the year for a general check-up/chat (which I imagine you would, but wouldn't know myself, so...), it can't hurt to ask them to prepare something for you around that time. In my experience, a lot of doctors are generally quite happy to write-up medical reports and just charge you for a usual session (and in that session, actually check-up on you as well). Sometimes, they're happy to write it up and send it through free of charge, too.
Having said all of that, though, I wouldn't worry too much about it. Applying for SEAS will become obvious when you get there. For now, just focus on doing well in school and keeping cool in the face of adversity, but with the knowledge that you will probably have a safety net.