Oh dear, J., you've sure got your hands full. It sounds to me like you're describing a sick, uncomfortable little person who doesn't really know what she needs to feel better. She's probably not sleeping as well as usual, or eating as regularly because of the illness, she could be a little dehydrated, all which can keep the brain/emotions from operating well. Plus she's got a new brother, and has begun to realize that's a permanent adjustment to her status in the family. (And what about teething – could that be part of the picture?)
Your little girl is not manipulating you in a planned, intentional way. She is, quite naturally, trying out every kind of behavior that might help her meet her needs, which, at her age and in her present state of health, are probably all quite legitimate. You can leave a sippy cup in or beside her bed and encourage her to use it at night. This might relieve one of your nightly disruptions, but if she's waking feeling generally miserable, it may not help much.
Of course, that doesn't help you meet your needs, but perhaps, as an adult who brought this child (and her brother) into the world, you can hunker down and make the heroic effort that's being required of you now. It won't last forever, it will only feel like it.
Hang in there. If you have a relative or good friend who could shoulder some of the burden of the new baby, this is the time to ask. Even a couple of hours help could make a positive difference for you. If there's something peaceful you like to do, like take walks or listen to music, try that, too. A few minutes of meditation or prayer, practiced several times a day, help many folks.
I would also like to mention that I've known parents who have had good results with homeopathic remedies. Pulsatilla might help if you'd describe your daughter as clingy and changeable (moods all over the place). Or if she's primarily just plain angry, then Chamomilla might be the best remedy. There are no side effects when used in the small amounts needed, and these are available inexpensively over the counter at many drug stores. If one or two doses don't result in a positive change, then stop treating, maybe try the other remedy. See more on this here: http://www.saskworld.com/bodymindspirit/edition23/do-it-y...