I have to disagree. I think it does get easier. Mine are 5, 3, and 1. The very first thing I learned with 3 is that I will not always be able to have the house cleaned up. When I had the 2 I would always have the house cleaned by the time my husband got home from work (between 6:30 and 7 pm) When my youngest was born there would be many times he'd come home and the house would be scattered with toys and cloths, etc. He never once complained-bless his soul.
When I was feeding baby I would have my 2 year old watch a movie, read a book with me, or even play with toys in his room. You also have to pick your battles more carefully. Remember you're feeding baby and paying attention to baby, so your 2 year old wants your attention. For example is it really important that she is running around the house? Is it going to hurt her?? If not it's ok until you're done with baby. That kind of thing.
I learned that I can only do laundry once a week (usually Saturday) because I just don't have time to do it everyday. And sometimes I would take the cloths out of the dryer and put them in a basket to fold while baby was napping. Also, when your 6 year old is well she will be in school, right? So during the day you will be back down to 2 at home. I understand taking a kid to school with other kids is tough, but it can be done. I take my 5 year old, drop her off, and watch her walk into the school. She is old enough to get to her class on her own. I will admit the first time I was nervous, but now she does great and she tells me each morning Mama I'm going to go in by myself, ok? I give myself about 5 minutes (maybe a little more) just to get kids in the car in the morning.
Another thing I learned is to make my 2 year old lay down for a nap. And if not nap than have a quiet time IN THEIR ROOM away from me for at least an hour. My babies usually napped in their swing during the day or in a bassinet in my room not in the other kids' room. I needed that time to unwind from the morning and get ready for the afternoon. Usually baby will take a nap at some point late morning/early afternoon that is longer. That would be my 2 year old's quiet time. I would have that time to myself to "recover" I don't clean/cook/ anything like that during that time. That is my time to relax, maybe nap, watch tv/movie, check my email, play a game on computer, read a book, do something that has nothing to do with kids or household chores.
The last thing (and maybe hardest lesson) I learned was that it's ok if baby cries! As long as all his (my youngest is a boy) needs are met he can cry for a couple minutes. If I needed to take care of something with the older kids it would be ok. I would put him in his swing so I could make dinner and many times he would fuss, but as long as I knew he had already been fed and his diaper was clean, etc he could fuss while I made dinner. I did make sure dishes were done, because you can't eat off dirty dishes, but I usually did dishes while dinner was simmering on the stove, or baking in the oven or something like that.
I hope this helps some. If you have any other questions you can message me. I have been there. I made it and you will too. Eventually things fell into place. In a couple months baby didn't have to eat as often and could be entertained by the swing, the boucer, or play gym thing, or tummy mat, or other toys/things. And then I had more time for cleaning and such and my house wasn't as much of a mess.
Oh... last thing... start enlisting your kids in help. I could have my kids at your kids' ages pick up their toys some. It may not be put away like you would do it, but at least they can put them in their room/playroom or wherever they beking. They can also learn to out their cloths in a laundry basket. That kind of thing. That will also help you feel better. Things are always harder when kids are sick. It's just something to push through. Most illnesses (unless it's something serious) don't last more than a few days and don't last forever! And I always worried about baby catching it. I changed my cloths if I had been cleaning up throw up, or cleaning up after a sick kid. I washed my hands all the time and certainly before picking up and/or feeing baby. That kind of thing. Good Luck and as I said I think it will get easier as time goes on.