Please talk to a counsellor or someone "professional" about this...not that we all here can't support you, but there are some deep things going on with your life, and your past that , imho, need more than we can probably offer, in terms of being face to face, asking the "right" questions, etc. My husband and I were in counselling a year ago, for things not nearly as serious as you are facing, and it helped us SO much. There must be a counsellor at your school, or a pastor at church, something. It also sounds like you are dealing with some verbal and emotional abuse that needs to be taken care of.
NONE OF THIS IS YOUR FAULT. You are only responsible for decisions you make, as in your words and actions. I know you feel like you have said the unforgiveable, but the key is that you KNOW it was wrong. You 1)acknowledge your sin, and 2)confess it to God, and 3)to the person you wronged, asking for forgiveness. God will ALWAYS forgive you, 1 John 1:9, If we confess our sins, He is FAITHFUL (he always does it) and just to forgive us our sins, and to cleanse us from ALL unrighteousness...As for your mom, it would be up to her at this point. You have said your piece, and she can decide to accept your appology and repentance for what you said, or she can choose to continue to hold onto the grudge, but you are free from that guilt, even though she may try to tell you otherwise. I know this is hard, pray for God's help to accept this.
PLEASE see someone about this. It is important that you deal with this stuff as soon as possible, because as you grow older, the effects of the abuse and neglect on your life and your health can grow exponentially. Trust me, I know a little from experience. It's important to deal with stuff as soon as you can. It keeps it from growing and festering more than it already has...I'll be praying for you. Keep writing here...I'll look for you.