Dealt with same thing. Unfortunatley, they learn quickly and as soon as you give in the habit is reinforced. It will take a few weeks to break the habit. Not easy. My daughter did the same thing - I was exhausted. Like yours, my daughter screamed for almost entire duration of waking hours. (As it turns out, she did have food allergies.) Try, again. You don't want to have to do this when you go back to work. You waited 30 minutes last night, try 40 tonight, then 60 the next, and so on.
Good luck and hang in there.
P.S.
After reading some other responses, I have the impression that some consider me a torturer. WOW! I am not saying to ignore her, do not repond to her, let her cry all night, or don't feed her. You need to sleep and if you have to work outside the home you will need to be rested. (Bosses don't respond well to employees arriving late because they overslept due to being up all night with a child.) I responded as I did given your circumstances outlined. Something has to give or you will come apart. Maybe you decrease just one feeding?! What works for one doesn't always work for another. Don't want you to feel guilty either if you can't co-sleep or continue with that many feedings throughout night by some other means. (You have addressed the issue with the peds and determined there is no health issue involved - like being underweight/not getting enough food.) Doesn't mean you are wrong, bad or insensitive, just means you have to handle things differently for you and your child. Last thing any mom needs is to feel guilty about choices she makes in caring for her child. Motherhood is a great club to be in - we need to support each other.