Let me start by saying that I do not think that you are a bad or selfish person.
It sounds like you are still grieving the loss of your mother and that you want to keep her memory very much alive.
Of course, it is a huge adjustment to see your father with someone else after all this time and it feels like this new relationship might mean that your father has forgotten your mother and moved on.
I think that it is important to speak to your father alone and tell him exactly how you feel.
You say that you know he deserves happiness and it sounds like this new relationship might provide that.
It does not mean that he has forgotten or cares less about your mother though.
Your shock will subside with time, and it is essential that you have support in all of this. I hope you have people to talk to that understand your feelings.
You are grieving the loss of your mother and possibly feel that you are now losing your father to this lady. You need to acknowledge the impact of this and allow yourself to feel your feelings without guilt.
There is no pressure to meet this lady until you feel ready and able, and over time as this shock wears off your feelings about it may change.
The main thing is having honest communication with your father and explaining how difficult it is for you right now. I wish you all the best.