Saying you are sorry and truly asking for forgiveness are two very different things.
Sorry = conveys you regret the incident issue but don't really take ownership of the place the other person is in.
Simply put we, as a society say we are sorry all the time. Sorry I stepped on your foot, sorry I forgot to take out the trash, sorry your team lost. It is a gesture but freely given.
To ask for forgiveness is acknowledging that you own the actions of the hurt. Please forgive me for putting you and our life in such a horrible place. I beg of your forgiveness that I have hurt my beautiful wife beyond words by my selfish actions and behavior.
Now, you are 3 weeks out so please be aware that she is most likely no where near being able to forgive you. You will have to accept this if you truly want to make things work.
Healing takes TIME. TIME - it is an ugly four letter word but it is so true. 2 to 5 years on average to truly heal from an affair.
If you love her buckle up. You placed her on the emotional rollercoaster from hell and you are going to have to go along for the ride if you hope to save your marriage.
Get her into IC, get yourself into IC and be present. You have to earn her trust back through your actions.
I pretty much told her you have every right to hate me and yell at me.
She knows this. She's acutely aware of this. Don't grant her permission as it will likely just make her more angry.
A great place for you to start is by reading:
How to Help Your Spouse Heal From Your Affair: A Compact Manual for the Unfaithful
by Linda J. MacDonald
It is a quick read and will provide you will a ton of insight on what your wife is going through.
Good luck. Prayers your way.