That's what a 3 day old does, and unfortunately that's how you can expect to feel about it.
Your baby spent 9 months in your womb. She was surrounded by the sounds of your body. During the day when you were active she would be rocked to sleep, at night when you were still, she'd wake up. That's why newborns typically have their days and nights mixed up. And those nights, not only are they far too quiet (white noise, for instance a fan, sometimes helps) but she also misses the constant embrace she had in your womb. (That's why swaddling sometimes helps.)
And then there's you. You just gave birth 3 days ago. Your hormones are plummeting, and this day is often when a new mother is affected worst by that. It makes you feel overwhelmed. It makes you want to cry. It makes you feel inadequate. No matter how well you are doing.
Just one thing: I'm sure you're a wonderful mother, providing your baby girl with everything she needs. But you say she's been cuddled before bed, and it just doesn't work like that. Imagine you're in distress and really really need to be held. Would that need go away if someone gave you a cuddle a few hours ago? Now imagine being a newborn feeling that need, and having no concept of the strain the other person is under.
I'm not saying that to fault you. I remember how hard this stage is. I only want to explain what this is like for baby, so you know her need to be held is not the result of you doing anything wrong.
With my second I got a cheap IKEA cot, took out the side, and put it next to my bed. Mattresses the same height. That way I could cuddle baby at night without the awkwardness of a barrier between us, while I could still keep my own blankets. It made a world of difference, and before you ask: yes, he still just grew out of needing this.