Oh man.

I have been there, and it's such a hard place to be. This inability to be everything to everyone became part of my PPD, so please be gentle with yourself. For me, the multitasking part of my brain broke when I had two children, and it took me over a year to figure out how to juggle everyone's needs - and honestly, I'm struggling again now that we have our third.
First, switch drs. If you feel there is significant need and they are ignoring you, you need to find someone who respects you as your child's voice.
Second, reach out. Swallow your pride, and ask for help from everyone you can. The house, the dishes, meals, the yard, the pets - give each person a specific job, and know that you have years of friendship to return the favor. if you can't find soemone to cover the dishes, use paper plates for a month. If you can't find anyone who can make meals, look into OAMC and make as many meals in one day as you can, when you CAN find help for a day. Even if you don't feel like the house/other stuff is part of the stress, for me having a clean kitchen felt freeing, so I could actually focus on the little people.
If you can find just one person, make them the designated baby handler - even an hour or two a week where you know she is safe sleeping in someone's harms, where you can get down on the ground and really reconnect with your son will make a difference. Does he do playdates yet? make a few, and give them a raincheck for hosting in a few months.
A swing, and a good comfortable baby carrier are great suggestions. Also, just know that
doing what you can when you can IS good enough some days. Both kids will probably cry more than normal while you all get settled, but
this is not forever. You are doing a great job - you obviously love your children deeply, and the day to day struggles have a way of smoothing out when you have that kind of love. Give it time, and be patient with yourself, and the kids. Everyone is new at this.