K.:
You poor thing! Fussy babies are so hard, and we feel so powerless to help. I understand.
You said in your post that you are breastfeeding exclusively. Two things: 1. Give her a pacifier if she's not already using one. Babies have a powerful need to suck. If she's not meeting that need while eating, she'll be cranky. Give her a binkie to use. Often what happens is she'll cry and cry and then you nurse her. She'll nurse to meet the need to suck, but she's not truly hungry. Now her tummy's overfull, and she's uncomfortable, so she's crying again, but for a different reason. 2. Try altering your diet. Babies care sensitive to what you eat when they are nursing. Eliminate something from your diet for a few days, and see if it gets better. Start with dairy, that's the culprit more often than anything else. Babies can't tolerate the proteins in dairy that transfer to breast milk, and they have stomach pain because they can't break it down. Give it a shot for a few days, and see if it makes a difference.
Colic is very rarely present after three months, because brain development moves them past that stage. If you truly think that's what's going on, see your pediatrician.
As far as sleep issues go, I'm going to give you a very unpopular piece of advice, and someone on here is going to tll younot to do it. Try it anyway. When your daughter wakes at 4 am, put her back to sleep, and then tuck her in next to you. Everyone worries about having to break habits later, but you both need to sleep NOW. My theory is whatever gets you through the first year is good, worry about later LATER. Sleep time is prscious, get it any way you can. Let her sleep in a bouncy seat or swing if that's what it takes for you to get enough rest. You can't be an effective parent all day long if you are exhausted, frustrated, and miserable.
Your daughter is old enough now for a baby carrier. Do you use one? I'm talking about the Baby Bjorn or Snugli setups. She may love one, since it keeps her close to you, and the movement of your body as you walk around may keep her content and leave your hands free to do things during the day.
My son was a half hour napper fr the first six months. It's maddening, I know. I used to play beat the clock during his naps in order to get housework done. I tried not to look at the time, and see how many tasks I could get done during the nap. So instead of saying he only napped for half an hour, I could look at it as he napped long enough for me to do the dishes, wipe down the counters, take out the trash, and sweep the kitchen floor! Sounds a lot better that way, no? It's just a mind game to keep your frustration level down. He would nap like that 5 times a day. I always dedicated the first one to getting showered and dressed, maybe breakfast if I went really fast.
You will make it through this. She will organize her sleep patterns into something that seems sane. All babies are different, though, so it may not be on the week that the boks say it will. My son, who was the original snuggler as a baby, is already almost 2 1/2, and giggles and runs away when I ask for a kiss. It seems like last night I was swaddling him in his blankie after a midnight feeding, but in a few hours, he'll be standing at the gate, yelling Pizza Pizza Pizza because he wants lunch, and is hoping to influence the menu. It all goes by so fast, and the stages breeze past. She'll be fine, and so will you.