Z.A.
Just a suspicion... but it sounds to me like you've got 2 very distinct problems that are combining to create the burnout:
1) Behavioral (throwing fits/screeching/not listening)
2) Sleep Dep (from nursing through the night)
The behavioral one is the "easy" one. You wouldn't let her act that way about anything else... right? If she threw a fit for not holding hands crossing the street/ wanting a toy/ eating solids/ etc., so why nursing?
This stage (to me) was the hardest. When they transition from being a baby (knowing what they NEED) to being a child (knowing what they WANT). I have a VERY independent & "imperious" boy. Teaching correct behavior & empathy & kindness, while encouraging imagination & independence & chutzpah... so not an easy task. Definitely a very loooooong task. :)
The second one, sleep dep, is harder. I am a HUGE proponent of "feeding on demand" (ahem... but not BY demand;) Physiologically speaking there is nothing better, and psychologically speaking the only better thing is to be living in a loving and supporting environment. I quit nursing at night though, before a year (he had bottles at night, before bed, in the middle of the night... whenever he woke until he was 5... and after he started solids he would sometimes have full meals in the middle of the night if he was in a growth spurt). At 7, he rarely wakes in the middle of the night anymore, but he DOES always eat right before bed. Milk at the very least. He's also pushing 5' tall (should be between 6'4" and 6'6" when he's grown)... so we're on the outer spectrum for how much and how fast he's growing.
Most children wake hungry during the night until they're at least 3. Some parents just let them stay hungry (which I don't get,,,WE'RE not building bone and muscle and nervous tissue... but if WE wake up starving we fix ourselves a snack, but they who are doing this huge amount of work, far more than we did while pregnant... they can just go hungry? In our wealthy, food abundant society? In every medical and psychology class I've ever taken, it makes it clear that abundant & healthy nutrition in the early childhood years is VITAL for proper growth and development. Every child rearing source I've found from the 1800's and earlier makes it clear that wee ones (if you have the food) eat 24/7 typically until their confirmation around 5 or 6, and STILL "a growing child needs to eat" was the standard. In the animal kingdom if a runt survives, they're usually the "fat" ones later, because they spent their infancy/early lives hungry all the time. The metabolism just gets set at starvation mode. But we do this to our kids on purpose? I just don't get it. Anyhow I digress.
The night feedings are harder, if the only source you have to offer is yourself. At least with solids or a bottle, you only have to be awake for about 5 minutes. I kept "easy food" and bottles that I could warm up on the door of the fridge before going to bed at night. (Actually if he was in a growth spurt and I knew it, I would wake him up for a bite and a change right before I went to bed... which gave me about a 75% chance of sleeping straight through). Anyhow, if he woke up I could stumble to the kitchen, heat up "x", stumble in & hand it to him... change his nappie while he ate... and then just kisses and stumble back to bed.
One q though... are you willing/able to cosleep for awhile? My son flat out refused until he was 3 (he liked his space, that one)... so I know it's not always possible.