Agree with what everyone else is saying. Be consistant. Just DO NOT feed her at night anymore, dont give in...EVER. If she screams and screams and screams for 10 hours and then you give in she will scream LONGER next time...if you do not give in consistantly for days or weeks she will get the idea. Have a strict time for feeding (I am not normally one for this but sounds like you need to do something drastic) in the morning and evening and if you want at nap time. Do NOT EVER feed her outside these times regardless of what she does. If you fold to her temper tantrums now it will get worse....a LOT worse and you will end up teaching her that the more she screams, kicks, whines the more likely she is to get something. Now its breast milk, before long it will be other things to the point that she will spend all day, every day screaming at you to get what she wants.
Personally if she was screaming and creating I would refuse, flat out, to feed her until she stopped crying, even at 12 months old that will have an effect...no way would I do it on a younger child but at a year they have enough grip on how things work to understand that screaming=nothing quiet=attention and milk.
I wonder if when shes screaming for milk you do a lot more with her, such as have her in your bed apposed to her own, fuss over her more, give her treats.....this will reenforce her screaming and screaming=good stuff.
Hope you manage to get it sorted, yes its hard to have them screaming BUT if you dont sort it now it will get worse.