It's possible for you to be friends if that is all you can be right now but you have to be able to separate your feelings from relationship to friendship and not have those feelings and urges to act as if you were boyfriend and girlfriend like you have in the past, with that being said I want to add that having her in your life at all is much better than not having her in your life and though it did seem a bit mean to leave you while you were sick and needed her most, she was honest with you about her feelings and that is all you can ask for though it hurts it will be easier to heal because you weren't left wondering why and if you are wondering why it's time for you to ask her why and what happened. She may be immature too immature to take care of someone that is sick or maybe she was afraid she would get mono from you, you really won't know until you ask if that is a question you want answered.
What I would do is first give yourself some time to grasp that you are no longer together, second don't take on the friends role until you know you can be just her friend for now, love her but not in a way that you want to be with her romantically, third when you think you are ready to be just friends give two weeks to make sure it isn't too awkward for you but if it is awkward don't try to lie to yourself and say your are okay with being friends if you aren't. Only do it when you are ready and able to separate the two. If you need more time then give yourself that make it on your terms and condition.