My baby was like this. I did have a partner, but she screamed every time she held her, she wanted to be with me all the time. She screamed constantly if she wasn’t. And she wouldn’t take a bottle and wanted to permanently be on the breast.
Although it remained challenging, there were a few things that helped.
Although she did not have TT, my son did - and the lactation midwife at the hospital maintained that he didn’t. So I would recommend a lactation specialist checking to ensure that baby is feeding efficiently.
I did end up reluctantly co sleeping , using the c shape and followed the safe co sleeping guidelines. Even so, she needed to be fed and cuddled to sleep and I couldn’t put her down until she was fast asleep. I would shift over and put her down where I had been lying, so the sheet was warm.
i learnt to feed lying down so even though she still woke and fed every 45 mins , I could doze. By the time she was 3 months old, she could access my boob by herself and often I wouldn’t wake. Obviously this necessitated my boob being accessible, but it was better than not sleeping!
Likewise, she screamed all day unless I held her and / or offered her the breast. So I carried her in a sling and again, she worked out how to feed whilst being slung . She napped in the sling too.
It transpired that she had sensory issues with clothes and she also screamed throughout every nappy change and bath. All I could do here was ensure that the clothes were all soft - just baby gro’s and vests, washed before wearing and all labels cut out.
i don’t know if any of this would be relevant for your baby, but some of it may help. I really feel for you - it wasn’t an easy time and I was exhausted, but it did gradually improve as I understood more about her needs.
(She is a gorgeous 13 yo now and she is still v attached to her mummy. But at least she sleeps well and by herself now!)