My younger two are twins, and only one of them was fussy and colicky and miserable. I can only just barely imagine having both of them be like that. I feel for you so much.
Having twin newborns is literally the most challenging experience I've ever been through in my life. It was hard. Really really hard. I was mind-numbingly exhausted, and struggling with constant feelings of inadequacy. I remember horrible days where I was so exhausted that all I could do was cry and cry, so there we'd sit, all three kids and me, on my bed and we'd all just cry together. I remember at one point telling DH that I thought maybe I had to give one of them up for adoption, because I didn't feel like I could do it.
It's really really hard.
First of all: you have to sleep. There's no way around that. A way has to be found, even if it means making some very hard decisions. Nobody's going to benefit if you go completely over the edge. And one good night of sleep will do miracles for your ability to think clearly and make decisions.
So I'd start by calling in any help you have, declaring that you're going crazy, and putting your foot down to your partner and saying you MUST have one good night of sleep. Choose a six hour slot during which you WILL NOT be disturbed, just for that one night. Leave your partner and whoever else you can get in to help with some bottles, and go to bed. Six hours is enough to clear your head, but not enough that you're going to get clogged ducts or seriously and permanently undermine your milk supply.
If you can't sleep with the babies in the house crying, can you check into a cheap motel for the night? I remember how hard it was to sleep, even when I was totally wasted, knowing my babies were needing me. But you have to be healthy to care for them, and you can't be healthy subsisting on a half hour's sleep a night or less.
Then after that, you may find that the twins and your DH had a horrible night, but I would guess that you will be feeling a lot more clear-headed and able to think about how to make changes that will make this easier.
And remember-- it's going to get much easier, and probably soon. For most babies, the colicky fussiness starts to dramatically subside as they get past three months and closer to four months.
Once you're able to think clearly, I'd start looking into a few things. The first would be milk supply-- have the babies' weight gain checked. Maybe rent a baby scale and weigh them before and after a feed, to see how much they're getting. Make sure that it's not hunger that's making them so miserable. I'd also talk to a good pediatrician about reflux.
Secondly, I'd start taking a good look at their daytime sleep. When babies aren't sleeping at night, and are miserable wrecks all the time, often the culprit is overtiredness and overstimulation. If they're awake for long stretches during the day, that might be the problem. A good rule of thumb is that if they're awake more than 90 minutes at any time, it's time for a nap again. Getting good daytime sleep will lead to less miserable evenings and sounder sleep at night.
Another thing to do is to start working with them on an alternate way to fall asleep besides nursing. Nursing to sleep is of course the most natural way for a mom and baby to sleep, but with multiples things get sticky. It really helped us to have the babies know another way to fall asleep. For DS, it was being put in the sling with DH and walked from the front door to the back while DH patted his bum and sang. (You should see a grown man try it!) For DD2, it was putting her in the carseat that fit into the stroller and pushing her back and forth on the front sidewalk, and then bringing the carseat inside.
What pump are you using? If you aren't using a double-electric with brand-new soft parts, then I would look into getting hold of a better pump. A pump with older soft parts may not be functioning optimally, and a single pump doesn't provide the stimulation that you may need to letdown for the pump. You can rent pumps from hospitals; just call the maternity floor and ask. Have you tried putting one baby on one breast, and the pump on the other, so that baby can stimulate the letdown reflex for the pump? Because my next suggestion is going to be a daily bottle of pumped milk. Believe me, I'm the biggest advocate for exclusive breastfeeding you'll meet. But when mama is going crazy, something has to change, and pumping a bottle is not going to be as undermining to your supply as formula, and is a lot better for the babies. If you designate a period of time during which you HAVE to sleep, and leave DH in charge during that time, at least you can guarantee a small part of the night where you know you will be able to get some rest. For us, we made it early-- I went to bed at 7:30, and DH stayed with the babies until around 10 or 10:30, when he brought them to bed and I nursed them. I chose earlier in the evening because nursing during the late-night hours is good for keeping up your supply. 2 1/2 to 3 hours isn't very long, the babies will be okay, and it's better than sleeping only like 20 minutes.
I found tandem nursing very difficult until the twins could sit alone. I just couldn't support their weight for very long, and nursing them both while lying down was impossible for me. I think breast size and shape have a lot to do with this. So another thing to do is to start teaching them to stay asleep when you unlatch. This is a tricky business, and it starts with learning to stay latched while side-lying. Work on that during the day when you're feeling more alert, because it can take practice. What finally worked for us-- I'd swaddle one twin tightly, and prop him on his side with two rolled-up blankets. (Tape them so they don't come unrolled.) Then I'd lie down on my side and nurse him to sleep. But I wouldn't get into full-body contact-- I'd have the rolled blanket between us. That way he wouldn't notice so much when I started to slip away. Once he was asleep I'd wait a long time, until he was barely suckling at all, and then I'd very very slowly move my body away from him, while staying latched. Then I'd unlatch really slowly by pulling away without using my hand. If he woke again, we'd go back to the beginning. Eventually if I was slow and subtle enough, he'd let go, then I'd slip away from him, going to elaborate lengths not to make a single sound, and I'd go out of the room and get the second twin and nurse her to sleep the same way. Of course if she cried, the whole deal was off, but with patience and persistence they did eventually learn the new way, and what that did for me was let me nurse them down one at a time. Then I'd sleep between them, so that I could pop the nipple in the mouth of anybody who stirred, before there was any crying that could potentially disturb the other.
It takes time and patience and there will be some days when it feels like it's all going horribly wrong, but it can be done and you will do it. Mamas of multiples are superheroes. After having done all that, I feel like I could easily do just about anything at all, because nothing else could be harder.
I can't write more now. It's 3 and I have to go to work. But hang in there, and if you want to talk, PM me.