I am so pleased that you have reached out and decided to come to the forum space and seek some advice and some support from people here that care for you and want to help you.
I am so very sad to read that at 14 you have all this to live with every day and that you are feeling like everyone hates you. That is really awful that your friend accused you of something and now people are ignoring you and making you feel bad, I feel like school is very hard these days and things like this do not make it easier. I can understand why you would lash out and try to protect yourself as you are hurt and these things are not true so you are angry and frustrated too. The thing that I found with school is though one minute something is hot news and the next minute it is not, until the next hot news comes along, if you know what I mean...I feel like perhaps your issue is inflated at the moment and you have lashed out and given them something to talk about but tomorrow it will be old news until somebody focuses on the next poor person who cops it...know what I mean? I am by no means discounting that you are feeling very sad and effected by these accusations but I am hopeful that it will not stay like this for long. Perhaps a quiet word tomorrow to your close friends to sort of say, hey sorry I lashed out yesterday but was just frustrated as the accusations are not true, I think they will understand and talk it through with you.
I am not sure about the words that your psychologist is using but I hear that you would like your "mood thing" heard and acknowledged as depression, I am kind of coming from the point of does it matter if you call it a mood thing or depression or a pink pig, as long as you are being cared for and heard and loved and supported I think that is the key here, and you are so wise and brave to come and reach out so I can see that your emotional intelligence too is way beyond your 14 years. I am so very proud of you for speaking up and I hope I can be of some help to you anon2005, you have come to the right place to be supported and not judged.
Hope to chat to you soon and big hugs to you.