Am I overreacting?!?!?!?!?!?

Basically, I was talking to this person over facebook (let's call him Jim) and we played truth or dare, He asked me to send naked pictures to him, but I refused because I hardly knew him and wouldn't do it anyway. His ex-girlfriend who doesn't like him (let's call her Amy) spread a rumour and told all my friends that I had sent these pictures. I didn't know she had said this until a bit later though. My friends seemed fine with everything, but at lunchtime when I went to the toilet, they ran away from me and rejected all 20 of my calls, I found them eventually and they just claimed they didn't realise I was calling them. We were just messing around, and I turned my back for a few seconds. I turned back and saw them running away. They left me in the rain in the middle of the school field on my own. I didn't speak to them for a bit after this because they were annoying me, but I got home from school and I got two texts from them. Amy had told them the rumour that I had sent naked pictures and they believed her. My friends who are supposed to stand by me believed someone else who doesn't even like them. I was annoyed and told them that I would never do such a thing, because I just wouldn't! I got annoyed that they didn't believe me and said loads of bad things to them. One of them apologised, one of them didn't speak to me and the last one just blamed me for everything bad that had happened in the world. I was even more annoyed and although I tried to forgive them, I just couldn't because they hadn't even told me why they were ignoring me. They didn't believe me and they ignored me. I didn't like them, and still don't at the moment, but I was just wondering, am I overreacting? They say I am, but I am so annoyed with them because they don't act like proper friends!!! Should I forgive them, or am I right to hate them for not believing me? I may forgive them in a few days, but I just hate them so much at the moment!!!! I have cried, cut and tried to jump out the window....(didn't work).....I feel like I would rather die than be friends with them ever again, because I doubt they will believe me ever again in times like these and so I just don't want to take that chance...