Hi, I can only imagine how difficult things must be having 3 babies under 5 years old. I have 2 under 5 and its a hand full!I hope my advice helps you out.
First for the breastfeeding, I had a similar issue with my second and it is very painful. The best trick I found was to really let my breast run under the hot water in the shower and try to massage the blocked glands to get the lump out and the milk flowing, sometimes a nice hot bath or even a really hot cloth on the breast will help, once the milk starts to flow a bit then try to massage some out so your breast can retake its shape and the little one will be able to latch on.
This is going to sound bad but you might want to ask your hubby to try to get it flowing, his suction is much stronger than the babies and he might be able to help you out, in a non sexual way ofcourse or not whatever works for you guys hehehehe. :)
As for the soreness of the other breast there is a wonderful creme called lanoline which was a god send for me, its non toxic so you can put it on and it won't harm the baby and it helps to heal the nipple and take away the pain.
Its normal to feel overwhelmed, you have 3 very small children,, I would recommend leaving the home for a couple hours here and there, take the smallest one with you because you're breast feeding but leave the other two with daddy and go walk around the mall or have coffee with a friend, do something for you. We as mommies all need some ME time, so take yours and don't let your hubby prevent you from doing it and if he does, drop the kids at grandma's and go out for a while, thats what I used to do :)
As far as your hubby wanting sex right now I'd let him know that although you love him very much, right now you need to be able to function and since you're exhausted its just not the right time, you will let him know when you're ready and able. Your body has gone through 3 pregnancies and births in under 5 years, you need some time to recoup.
One thing I used to have to tell my hubby a lot was, if I get rundown and can't function you will have to take care of all the household responsabilities, that usually made him realize just how burned out I was or am and then he'd leave me alone for a while. Ask him to cuddle for the time being, you want to be close but not sexually close right now, let him know how it makes you feel, and you don't want to feel like its a burden that you have to do just to please him. I'm sure he doesn't want that either.
One last thing, your other 2 daughters need daddy right now, they will get all of mommy once mommy has had the chance to recoup and take care of the little one. Don't feel like you're neglecting them, you don't have a choice right now and in the end they will have you, it will only take a few more months to get everything all balanced out, until then ask your hubby to be more involved and to keep them busy, or if you can afford a bit of help have a nanny over a couple days a week to play with the kids. Since summer is around the corner you can probably find a young girl to come play and make lunch and that kind of stuff so you can regain your strength. The kids are very young right now and they'll have fun playing with daddy or someone else. Explain to them that mommy loves them but you're very tired right now so you got some help, or daddy is going to help...they'll kinda understand, they'll probably want to help you out too.
Wow this was long and I hope it helps a bit...I wish you all the best...
E.