C.M.
Don't try to quit cold turkey. It will be harder for her and you don't want to risk the engorgement problems. If she will take a sippy cup then you are already on your way. She is to old for a bottle at this point anyway. Cut out one or two feedings at a time and then wait a few days before you cut back again. It sounds to me that she wants to nurse for comfort reasons and not because she is actually hungry. You might have to handle a couple of tantrums before she gets the idea that mommy is now longer going to feed her on demand. She is old enough to understand but that doesn't mean that she will like it. When she wants to nurse, maybe offer her a cup of milk and sit and read a book to her or something like that while she drinks so that she is still getting that mommy time and the attention that she wants but not the nursing. Don't give in to the tantrums! That will only teach her that she can act badly to get what she wants. If she won't stop screaming, put her in her bed and leave her alone to work through it or something like that. Whatever works best for you. Let her know that you are in charge, not her. Be firm but loving and she will figure it out. She will need a little extra attention for the first little bit but once she figures out that mom will not feed her anymore, she will move on to other things.
As fas as the lactating goes, I still had some milk for a month or two after my youngest weened but it will go away eventually.
I hope this helps. Let me know how it turns out.
C.