Ahhh love, it gets easier, you know it does. I had a newborn and a 9 year old, dh (temporarily) turned into a cockwomble and was also working away monday to friday from baby ds being about 3 weeks old. I had no car, public transport was shite and besides, no point going anywhere cos ds would just scream. I was ebfing, semi cosleeping, recovering from a c section and I have never felt so alone or so vulnerable.
A sling actually saved my sanity. Not ones of those fancy bits of fabric that would have just been more stress, a caboo close I think it was, followed by an ergo when he outgrew the caboo.
I also joined slimming world and started eating better and losing weight. Plus I loved the social aspect. Know things are obviously different and you are probably a skinny minnie but just something once a week just for you as soon as you can.
An hour slot once a day for a nice long bath, hairwash, dry your hair etc will make you feel better, 1 to 1 time with your 6 year old to watch a bit of telly or read together and a nap whenever you can. Are you bfing? If not go to bed early and leave dp up with the baby.
It will get better. I found 4 weeks to about 12 weeks incredibly fucking difficult. But it's a temporary thing I promise.