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1.You saw her way too often and invested way too much, way too early.
The way to know if you want a real relationship is to have sex at the latest by the 3rd time you see her. Any later and you're flirting with AFC boyfriend (she withholds sex, expects you to pay, cancels, comes late, ditches you for her friends, cheats on you, etc) or straight up LJBF territory.
You should keep things casual by only seeing her 1-2 times a week initially, until you really feel there is a connection and you want to get more serious. Then you can choose to commit to her exclusively. Why do so any earlier, you barely know each other?
Keeping yourself less available also makes you a higher value commodity (simple economics) and therefore makes her want you more.
2. You let her know exactly how you felt and laid all your cards on the table.
If you want a girl to be really into you and constantly thinking about when she'll get to see you again, then you have to keep her guessing. Keep things interesting, invite her out to fun stuff, and DON'T let her know exactly how you feel, what your goals are, and where things are going. That keeps her wondering, and working hard to keep your attention and keep things good between you.
Your ultimatum makes no sense because you're arguing from a position of 0 power. You've raised the relationship question and started trying to guilt trip her into wanting to be with you. You've clearly invested more emotion into this then she has, and now you're not even having fun. You're offering zero value and then making her choose you. I wouldn't take that deal, would you?
You're trying to change her mind instead of her emotional state. The way to get someone to want to see you is not to say "hey I really want you to see me," it's to just having a fucking awesome time and make sure they enjoy themselves around you. If you do that, they will want to do it again.
Conclusion: You're in college, for fucks sake - you should be going out and meeting tons of chicks, you do not need this specific one. Relationships are pretty casual and you shouldn't feel the need to tie yourself down to one girl, especially so early on in getting to know her. Play the field, keep things more casual, and wait to hold hands and see her frequently until you've been going out for a while first.
As tough as that was to read about all the mistakes I made, you are 100% right...I fucked up from the start and I did this because instead of running proper game, I was just excited by the fact that I was seeing this really hot, cool girl. It looks like your conclusion is the right thing to do; however, my problem is that I go to an extremely small college and the number of hot girls is very far and few in between.