K.D.
I haven't read other responses, but wanted to give you some thoughts. I nursed my second child and she screamed a lot the first 4 months. People brought up that she probably had "colic," but my observations showed no evidence of that or any other acid reflux or gas issues, and my gut instincts said she was fine. Looking at her now, I believe it was her temperment. She's extremely spirited and active and quite animated in all degrees of expression, whether in elation or utter despair. But that was a very, very stressful time. Someone during this time asked if I had PPD and I didn't think so because if she was fine, I was fine and actually happy. Mine was circumstantial. If things were blissful when you got home, maybe this is stress related and not hormonal. But, I know hormones are changing during this time, so it could be that in your case.
I think your eldest is really craving some loving attention. Not only is there a new baby in the house (your eldest is not your only focus now), but there's a lot of stress in the house with the baby screaming so much. And with you being stressed, it adds even more stress. I feel badly for how short I was with my eldest when my second one was first born. I longed to spend more time with her, but couldn't cause I was taking care of the baby.
Point being, do you have anyone who can come over and hold the baby? Can your husband give the baby a bath or hold her while he's sitting in a chair? I'm sure he's wiped out from working, but you really need him during this time. It takes both of you to work together as a team. My husband helped mostly with our oldest during this time. I wanted so much for someone to come give me a break with the baby, but everyone said, "Well, I can't take her, cause I can't feed her." They could have come over and held her or bathed her. But those closest to me where we live, were not favorable to breastfeeding, so that caused misunderstanding as well.
I do think you need a break. A few minutes here or there are so vital. I used to put my youngest in her car seat in the bathroom with the fan on. It seemed to help calm her. Some people don't like the use of a baby swing, but if it helps and it can give you a break USE IT! They now have playyards with vibrating bassinets. Would have LOVED to have that. Whatever works. This is sanity survival mode.
And whenever you can, give your eldest daughter tons of hugs and kisses. She would probably sponge that up.
Well, those are my rambling thoughts. If you want to contact me, please do so. I'm here in your corner!!