Hi,
Sounds like what you've got is a normal baby. Still, doesn't make it any easier for a tired mum with another child to care for. Just over a week ago she was in your tummy, always held, always fed, always hearing your heartbeat. Life on the outside isn't at all what she was accustomed to. she is hardwired to be close to you - she wants "womb service". Some babies make the transition easier than others. The good news is that is won't always be like this. She will get the hang of it. But right now it's you she wants, and she is hardwired do suck and be in contact with you. As you've rightly identified, she doesn't need more milk.
since she is feeding well, you might consider using a dummy after feeds to help her settle. sucking releases hormones which help babies sleep and relax. Baby slings are fabulous. If you don't drink, smoke or take drugs, and you make your bed safe it's OK to sleep with her in your bed.