You are not in the wrong. You are not a burden. You are not pathetic. You gathered so much courage to open up. And you have been trying as hard you can. So, it's okay to let the tears out. Your mother cannot just simply deem whether or not you are suffering from mental illness. That is the role of a professional. Your mother might have gone times that weren't all sunshine or rainbows. But that does not invalidate your struggles.
You seem to be aware of what you are going through. I hope this experience won't deter you from seeking for help again. You might not want to tell other your friends, but you deserve love, care and support too. What would you do if you knew your best friend was going through terrible times alone?
I will also add that many people are here can empathize with this rejection. I remember crying on the bus when my dad told me I was lying. It hurt even more knowing he had seen me cry every night for months. I came to terms that my parents won't understand mental health issues due to their upbringing. It has been two years now since that day I cried on the bus. Things have not magically improved, but I see that my parents are trying to help (although sometimes, it can make things even worse).
Take care