You aren’t in a relationship, but yet you are getting upset, hurt and angry as if you are in a relationship. That’s why she lied to you. Because it wasn’t any of your business.
She’s probably well aware of the fact that you like her in a romantic way. She probably does not feel the same way about your or else she would have said so, specifically. She probably aslo realizes that because you do live so far away, that there is no chance of you guys ever being in a “real” romantic relationship. So she if free to socialize (and kiss) guys who are in her town.
She probably also enjoys skyping with you and even flirting with you. What she doesn’t realize, is that by doing that, she is encouraging you to have deeper feelings for her, which will never be brought to fruition because of your long distance problem.
I would just be very calm and simply say something like, “Hey Carmen, you said you didn’t hook up with anyone at the party, but there’s a picture of you kissing some guy on Facebook. Are you guys going out?” Then let her answer. She may say that she’s not going out with him and not tell you anything else. Don’t push her to tell you more if she doesn’t want to. That will only make her defensive and she might become angry with you. Or she may tell you the whole situation.
Whatever she chooses to tell you, don’t get mad, don’t get weepy and DON’T act like you are her boyfriend. Just say, “Oh.”
This is one of those situations in which you have fallen head over heels with an un-available person. You have to decide whether you want to keep up the charade of continuing to skype with her (and continuing to feel love and getting hurt and feeling jealous) or cool it. If you can manage to get over your lovey-dovey feelings for her and just be friends then make sure that when you skype her, you keep it in the friend zone and out of the boyfriend zone.
But I’ll let you know that when one person feels love and the other person feels only friendship, the relationship is likely to come to an unpleasant end. Long distance relationships usually end badly too. Your best bet is to find a girl that you like in your own town. Don’t sabotage your romantic efforts by looking for love in faraway places. It may be fun and exciting for awhile, but it’s not practical. Feel better : )