I'm so sorry that she's not sleeping well - which means you aren't sleeping well! Such a tough place to be :(
Based on what you said, it would appear that you are opposed to letting her cry. I can see why you'd feel that way, as it is SO painful to hear your tiny baby cry. I absolutely hate hearing it. But after having 2 babies myself, I have learned something. You are doing your baby a favor by letting them cry, because they learn how to fall asleep on their own.
I truly believe that when you are constantly trying to soothe and stop your baby from crying, you are basically never allowing them to fall into that deep sleep. And then they are miserable! (and you are miserable) I decided to try the cry it out method, and I was so nervous that it was going to be just awful. And honestly, it was at first. But then I realized that she only cried for about 5 minutes, then fell asleep. Truly asleep :)
It occurred to me that when I was rocking her/singing to her/nursing her when she wasn't really hungry - I thought I was helping her and soothing her, but I was just distracting her from sleeping.
They learn to fall asleep quickly. The crying feels like it lasts a long time in the moment, but if you look at the clock, its usually only a few minutes.
Please know that I support any mom who is trying her best - I am NOT here to bring judgement. We have to go with our gut and follow our instincts and I have no doubt you are an amazing mom. But I thought I'd share my own experience. I would encourage you to think about it and maybe ask around to your doctor or other moms.
Good luck!