I wish that session had gone differently for you. I don't think downplaying your struggles and comparing them to your mom's was an effective choice on their part. Your pain matters. Your self harm matters. It doesn't matter if there are no marks on your skin or are very severe. Self harm is an issue and you deserve help.
It's perfectly understandable that you feel the way you do. Would you feel comfortable telling your therapist and mother how you feel? I think it's very important that you have the chance to work on coping skills and why you want to hurt yourself.
I wish you the best. Feel free to message me if you ever want to talk!