It definitely gets better OP! You are doing a great job 
My DS was exactly like this when he was tiny but he quickly turned into the most placid content baby you can imagine. You have both been through quite a big shock, giving birth and meeting each other for the first time. Being a mum is a massive adjustment that I don't think anyone can be prepared for, so just give yourselves time to get to know each other and you'll work out how she ticks soon, I promise.
@PenguinJS has given a good list to work through when she is upset and I'd second skin to skin to calm her. I always think it's funny that you do it in hospital but not many people do it afterwards, it is extremely calming for the baby to feel you, hear you, smell you etc.
I also found when all else failed getting out of the house with DS in the pram helpful. He was always quite calm in the pram and I got some fresh air which helped clear my head. I always found it was actually better to get out when I'd had a terrible night, even though I was knackered I always felt better.
Please ask for help as well. It sounds like you have a good support network so don't be afraid to say that things are hard because people will often want to help but won't want to be overbearing.
Just worry about getting from one day to the next, so much changes so quickly when they are this age. Have faith that mum knows best and you're doing everything right.