How to get through with an unsupporting supervisor? My supervisor does not have time to neither read my report nor give me feedback. The topic I am working on is totally new and my supervisor does not know about that. 

There is another guy in my group who works on the same topic. I got the correct result and the other guy did not get the correct result but my supervisor believes the other guy and made me feel very bad by implying that I made up the data. Even if I show her my solution, she will not be able to understand or simply does not want to admit that I am right. It is not an easy feeling for me when I am in group meetings, I have to shut my mouth when the guy says wrong things. 

I like the topic and I want to continue work on that but I really need to get over all the bad feelings. All other professors in my university working on that topic have some kind of collaborations with my supervisor so it is not ideal for me to change supervisor.

Has anyone been in the similar situation? How would you get over that and become successful?
Show your supervisor why you are right and the other guy is wrong. Gather solid proof, wait until you are less emotional, ask to meet your supervisor and tell her in a neutral, professional tone. Maybe she just wasn't able to see your point at that moment.