crucially I am missing out on making some much needed mum friends in the area as I can't get out to any of the meet ups I'm invited to.
Seems like you're putting a fair bit of pressure on yourself. Relax, 5 weeks is such early days. You have lots of time to meet other mums and do groups etc.
At this stage I'd advise simply following the baby's needs and letting other people help you as much as possible. She's still so little, all she wants is the reassurance of mummy. Have a read about the 4th trimester, it was a real eye-opener for me.
On a practical level, can you ask someone to do a shop for you and stock you up on ready meals, cereal, instant noodles etc? Basically things that can be made and eaten quickly or one-handed. Since she can't really go in a sling, do you have a bouncer you can bring into the kitchen with you while you make yourself meals/snacks? And she can sit in that while you're in the shower. I understand not wanting to put her down because she cries but at some point you HAVE to take care of your needs too. If she's safe, been fed, in a clean nappy and is in the room with you then don't feel bad leaving her to cry while you wash your hair and enjoy a scrub.
DS likes to have a Muslim square beside his face while he sleeps during the day. God knows why but he sleeps longer and is much calmer when he has one there. Also, when putting him to bed I take off the top I've been wearing that day and wrap it round the mattress in his Moses basket so he has the comfort of my smell. We've found he wakes less in the night with that there.
My MIL suggested infacol in the bottles because he wasn't getting wind up very well and was having real problems with trapped wind. It's worked a treat, although we only put one dropper in every other bottle. Also if your DD kicking her feet quite hard and a lot that could be a sign of trapped wind/ discomfort.
I cried with relief when someone gave us a vibrating bouncer and DS finally allowed me to put him down for short periods without crying! Also getting out for walks is good because he enjoys the motion of the pram and will be quiet for most of the time we're out, you could give that a try.
Don't be afraid to ask people around you for help. There's this perception that having a baby is all about instincts and you'll know what to do and how to do things. It's not true, parenthood is a huge learning curve for most people and I don't think we (humans) were meant begin motherhood in the isolation we seem to have developed into. It takes a village to raise a child, let people help you.
Sorry for the essay but no one told me these things until he was here and I was struggling so just want to pass on as much help as possible. DS is 13 weeks and I've learned these things in that time.