Hello C.,
I am a stay at home mom with two children (5) and almost (3), with a husband who owns his own business and works full time.
Your 4 month old sounds like my experience with my daughter who is now almost three.
Crying is okay, but if your daughter is screaming that means that she really needs you. The house work can wait. When your daughter is 20 I guarantee that she will not need you in the same way, so enjoy these precious moments.
I eat organic food, do not own a microwave, and enjoy a nice homecooked meal, but investing in canned meals, frozen meals, and pre-packaged meals will give you more opportunities to eat dinner in a timely fashion. You will only need to do this for a year or two, and then you will be able to get into a regular schedule. As your daughter grows older you will be able to find time here and there to do more daily house tasks.
Asking the hubby to do house chores and cook dinner once or twice a week can be helpful as well. Your spouse wants a happy momma.
Have a friend or family member create a food tree or house cleaning tree where your friends and family members come up with a schedule to commit to bringing your family a home cooked meal once a week and/or come over to clean your house or hold the little one while you clean the house once a week or every other week.
Patience, communication, and respect will grow between you and your daughter as you grow together.
The time that you are investing now to meet your daughter's needs will build her self esteem. She will know that her needs will be met when she needs it, and she will learn that you have needs as well and she will learn to be able to facilitate in creating that space for you as well.
The best of luck to you and yours.