I’m so sorry to hear this. It’s sounds really tough right now 
I’d say take it one day at a time. Small steps. Please know it’s just a phase, this is the tough black hole of parenting where you feel sucked in and unable to get out. I’ve been there. I think most of us have in one way or another. But you will be okay. You’re not alone.
Lack of sleep is a terrible thing, so try to do a few things to help that could work with your hours. What time does you OH get back? Can he take the baby from then so you can have an early night? Warm drinks, hot baths, lavender oils can all help. Getting some exercise helps too. It’s daunting, but if you can take baby out for a walk every day it will help.
If you’re getting intrusive thoughts, remind yourself it’s just your anxiety. If you’re really struggling, call Samaritans. It’s always good to talk. Try anything to keep your mind occupied like reading, painting, or play some music. It’s amazing how much being creative can help.
Your baby loves and needs you right now. If crying it out isn’t working, that’s fine. Instead, cuddles, walks, put her in a sling and do things. Dance and talk to her. Tell her how much you love her. Listen to those cries and tell her you understand. I promise, it really helps to calm you both. If it’s too much, put her down safely in a crib and take five. Make a cup of tea. Go back and have some more cuddles.
If she’s crying for no reason, it could be teething or something else. Get her checked out, and take the opportunity to get yourself sign posted by the doctors.
Re childcare, can you get her in nursery just once or twice a week? Anything to give you a break and to give her some stimulation will help.
You can do this! It will be okay and you will look back in a few months and wonder why it was so tough. Keep posting, talk to people IRL. Tell your OH too. When you can, try and spend some time with each other just to reconnect and share your thoughts, get that support you need from each other emotionally.
It’s going to be okay x