My Former employers discriminated against me and I have no idea on what I should do.

My former employer unfairly dismissed me. They held a meeting when I was dismissed and raised all of their points against me, however, most if not all the points were not true and were false allegations. I did not want to argue with them during the meeting but instead decided to take my case straight to HR. Initially, my former manager told me all my concerns were to only be raised to him but I demanded that I either speak to their manager or to HR in which he gave me the contacts for HR. I raised all my points and concerns to HR and they held a meeting with me about it. They then emailed me their response weeks later and rejected my appeal. Once again the points raised against me were not true and innaccurate (i.e. I took a leave early December and they said that there was a complaint made a week after my last shift and somehow I was held accountable for it despite not even being on shift at the time). Pretty much every single point raised were not true and honestly speaking I'm very distraught and upset at the moment. I don't really care about the job and don't want to work for them anymore anyways but it upsets me how people find it acceptable to blatanly discriminate against someone like this I wish I could find a way to find justice but I just have lost hope and trust in anyone. I thought HR would at least be managed by decent people who wouldn't falsify things but they did and to make matters worse in the email they said "this decision is final and there is no further right of appeal." I'd even like to take things further to a court but they have all the evidences and can easily change it (such as shifts and the work completed). On the day of my dismissal I requested to recieve the sources so that I could gather my evidence but my former manager refused to allow me access and said I didn't work for the company anymore. Also, on my contract it says that I have a one week notice period, but I was not paid for that week despite being entitled to it. I also raised this concern of which they said I was paid but the numbers don't add up I was only given my extra 'holday pay' not the week.