Kiwi that sounds so so tough. I agree with LadyT that some babies are just more relaxed than others - some are very highly spirited and always on the go.
You mention that she obviously doesn't need to feed continuously at nursery and manages well there. i wonder how they find her "behaviour" (lol, she is only little) there. ie does she "scream" a lot there? It is very common to have the angel elsewhere/devil at home.
If that is happening I would suggest (and I am sure others might disagree) that you have got yourself (very understandably) into a viscous circle of "she screams, you feed (which is of course lovely)....then she realises that screaming means boob...which results in more screaming".
And that has come to define your relationship more than you are comfortable with. From your post, it seems you are looking at it from the other perspective - ie "what would I do about the screaming if I didn't have the option of bfing her".
I would suggest that you pick, say, four times in the day that you are happy for her to have a feed at - and at those times she is picked up and offered a lovely cuddle and feed - and then at the other times she is given something else to do/eat/drink. Yes, she will scream, but ime, (if you stick to it - and are you sure you are strong and want to do that)you will break the habit in three days. Once you have a "new" pattern established where she doesn't associate you with constant feeding, then I am sure you could have more flexibility to feed whenever you/she fancied. But it seems an awful shame to give up b'fing her, just because this pattern has emerged.
I don't know if this is making any sense, but my friend (who is a lovely child-centred) child pyschologist describes a lot of the problems of early years (early waking, continued night feeding - when Mum not happy to do it, children not going down at night) as "slot machine" problems - ie we respond in a certain way once or twice to a behaviour by, for example, giving a bottle of milk - so the child (very naturally, not because they are horrid manipulative beings) associates that behaviour with getting something nice. And then that behavious gets entrenched.
I do have a tough time with my DD2 perpetually wanting to be carried around. Now of course I am happy to cuddle her and carry her - but just not all the time, I have two other kids to look after. So sometimes I have to let her scream while I get on. 9/10 she then gets distracted and poodles off to do something else. She knows that screaming won't yield results. When we have had doting Granny in the house (who has the time and inclination and of course should) lifts her at the first screech, then I normally have a couple of days when I have to reestablish - sorry but I can't carry you everywhere my darling.
Anyway, ignore me if you think I sound like a cold-hearted person. But I personally think that at this age they are not teeny tiny babies who need to be fed nonstop, so nutrition isn't the issue, cuddles should be given in abundance but if a mum is at the end of her tether with either night wakings or constant feeding then it's in everyone's interest to break the pattern. I probably sound like Supernanny. Lord help me.