Stop seeing her immediately! If you feel this way after one session, additional sessions will just reinforce it. It is highly, highly unlikely that anything good will come of going back. Most likely you'll get hooked on the feeling, spend a lot of cash, and either begin to want more or run out of available cash flow and literally crash when you can no longer get your fix. Appreciation and enjoyment is one thing in this industry, but falling in "love" is to be avoided. Keep in mind that an escort's livelihood depends on you having a good time, so she will say and do almost anything to make it so. It'll make them act differently than if you just happened to meet her say on campus.
I show no signs of love interest when I'm there, I make sure of that. I want to but know that it would be a bad idea to. I am thinking of seeing her one more time and asking if she would see her clients outside the agency, worth a try IMO.
And no, it's not worth a shot IMHO. Even if she agrees, you'll lose. She'll continue to see other men. Is that okay with you? No really, think about it. Are you okay that she's seeing other men, not only to fuck them but also discussing their personal lives, flirting with them, and pretty much having the same experiences you had with her? Escorts on here have lamented about how hard it is to have a relationship in this industry. They would know best, and several of them are here in this thread telling you to run.
What you are feeling now can also be experienced with a civilian girl, and it has much less potential for disaster. Stick to your campus until you're older and wiser emotionally. Good luck!