What a mess! I’m so sorry your mother’s relationship with you and your sister has deteriorated so much. I’m guessing that everyone in the family is feeling emotionally fragile and exhausted. Believing your troubles are your boyfriend’s fault may be a way your mom protects herself from feeling responsible. Worrying you and threatening you and your sister tells me she is feeling bankrupt. She just doesn’t know what to do with two teenaged daughters. She’s stressed. You are stressed. I suspect your sister is too.
I agree that lying about seeing a psychologist wasn’t the best way to get the help you need. But it looks to me that taking charge of getting some help for yourself and maybe your family was a healthy move on your part. Please talk to your psychologist about all you’ve told me. Ask if you should transfer to a family therapist so that you, your sister, and your mother can work on creating a more peaceful home during your teen years.
You didn’t mention your father. If he is in the picture, he should definitely be included in such counseling.
I wish you well.