My experience of dealing with friends that have just been given the big boot from a first love, is... they never take your advice.
They always go running after their ex, crying and grovelling and offering to change themselves as if it will save the failed relationship. Essentially, in my experience I've found this is exponentially worse when they are a) young b) first love.
No matter what we say to the OP, or what the OP claims to have done, I can bet you £10 he's there begging his ex for "another chance". It's the age-old case of denial. Usually the longer they've gone out, the worse the backlash.
You need to chalk this one up to experience, and know that you got played. Move on from her, do something constructive with your new found free time and resist the urge to contact her begging for x,y or z. Once you accept that you've done nothing wrong (except for paying for her uni fees!), and that she chose to end the relationship, you'll always have the morale high ground over her.
Think of it this way. Do you want to beg this ex for another shot of a relationship that will never truly heal, sacrificing all your dignity and self respect whilst her opinion of you goes down the toilet and that getting back with her is just going to paper over the cracks of a relationship that will probably fail, or do you want to learn this lesson and be able to look her in the eye in 5/10 years and know you were man enough to stand up for yourself and move on? I know which one will get to her the most, although don't think of this like a game. Playing "one up on the ex" will lead to you banging her sister, and then that bridge is well and truly burnt.
Who knows, you may part amicably and get back together in 10 years, if it's meant to be.
This doesn't mean you can't express how gutted you are it's over. I don't believe anyone can truly advocat a terminator-like approach to getting dumped, but at least if you tell her how's she made a mistake etc etc and move on, she will be the one that will come to regret it when she looks back on the relationship, which won't happen if you spend the next 2 months stalking her, calling her or generally begging her for another chance.
She probably is seeing someone / has met someone, and wants to try things out while you're kept on the back burner, so don't rule that out.. after all, she's been letting you pay for uni, so it's not a stretch to believe she's shafting you physically as well as financially, although she will never admit it, and trying to prove it will drive you crazy and/or get you in to trouble.
You're going to feel like a mug for a while, and you'll probably get that sick feeling from the anxiety / nausea of your "Stable" love life being torn up, but that's only natural. You won't be the first, or the last guy to go through this, so essentially, you need to try and carry on as best you can, and as normally as you can.. go to work, go out with mates and if anyone asks just play it down.
All the best.