Only Your Ex Knows If It's Over
You're wondering if it is really over between the two of you; unfortunately, there is no way anyone -- except maybe your ex-girlfriend -- can answer that question for sure.
Examine Her Breakup Motives
But her true motives for ending the relationship may help you determine if there is real potential for a future together.
Her apparent reasons for ending the relationship are very understandable. Medical school can be extremely overwhelming and time consuming, and long distance relationships can also be very difficult. But it sounds like you may have some doubts about her real motives for ending it.
If Circumstances Change
Perhaps you should seek to find out for sure what her reasons were, and then determine if there is still the potential for a romantic relationship. If she ended it because of the difficult circumstances (medical school and the distance), then she may be willing to pursue a relationship when her circumstances change, especially if you develop a close friendship in the meantime.
You Can't Force Her To Love You
However if there is a deeper problem here, or a true lack of interest on her part, then you need to accept that. You can't force her to love you, and your friendship should remain just that -- a friendship with no strings attached or ulterior motives.
Will YOU Take the Risk?
The fact that she is continuing a friendship with you and that you talk every day on the phone means that she has not completely shut the door. There is hope; I think the main question is: Are you willing to take the risk in continuing the friendship (i.e., risk getting deeper involved and possibly opening yourself to getting hurt even more down the road) for the possibility of a future relationship? And how long are you willing to wait? You need to be honest with yourself (and her) and determine whether you can develop a "no strings attached" friendship with her, and are willing to take the risk.
Waiting Strengthens Relationships
I believe that strong relationships are often built on a foundation of friendship. You need to be patient with her. Don't force yourself on her, and don't give her any kind of ultimatum.
I wouldn't throw away something that has potential just because you're not willing to wait for it. Plus, this waiting period would probably strengthen your relationship anyway.
No Hidden Motives
However, I would not continue a friendship with the hidden motive to turn it into something more or to "make something happen". If you have other motives, they will be discovered eventually, and it will cause more frustration on both sides. You need to respect her feelings and her situation right now.