I feel bad without a reason

Hey, I've been feeling pretty bad lately and I just need to let it out somehow. I suffer from social anxiety and probably more than that and it's been really holding me down for almost a month (it's been holding me down before, but I am at my worst right now) . I had a breakdown a few days ago when I basically told my mother that I have problems but she just doesn't even care (even though I know that's not true). I love her, don't get me wrong, but... she just doesn't understand why I don't have many friends and don't want to meet new people and she sometimes tells me that I shouldn't be at home all the time and the last time I just... kind of blew up. I am stressed out from school and to be honest, the only thing keeping me here is my pets which I love more than anything. I think about suicide even because of the smallest and stupidest of things like grades, my future, when my parents yell at me, stuff like that. When I get bad grades, I immediately think about how I am going to fail and that if I failed, I would have to live with the shame and I would have to meet new class and I would kill myself rather than that. When I get yelled at, I feel that I don't have to be here because the people around me don't even care about me and would have better lifes if I was dead. I am sick and tired of how nothing ever happens and everything is the same. I get up in the morning, go to school, go home, sleep, repeat. The same is going to be when I go to job. Today is my birthday and one of my friends came over to say hello and give me a little gift. We had a nice conversation for around two hours and I told her how I feel and she told me how much she loves me and that she doesn't want me to hurt myself. We had a talk and she really helped me feel better at the moment, but once I got home, I just regreted that I didn't tell her how much she means to me and I feel that I am not good enough. One part of me tells me this all is not true, but the other one keeps saying that I am just a stupid little thing and I will never be good for anything. We have a big math exam tommorow and I think that I do not know enough to pass with an okay grade and I am scared I am going to fail. Sometimes when I get mad, I imagine hurting the person I am mad at very bad. I am afraid one day I am going to hurt or kill someone. Sometimes I let out my rage on random people and then I regret it. I am probably going to go to a school psychologist. I don't know what's wrong with me, I just want all this to stop. I want to live my life like my peers do, but I just can't. I feel broken.