My suggestion first off is to get a baby carrier like a hug a bub or peanut shell.
This will allow her to be close to you like she craves and give you more freedon to use your hands for other things.

She is still so little and the independence will come with time. Being prem may also be contributing - she needs the safety and security that being in your arms provides.

I know it isnt easy when they wont let you put them down but she should get better with age.
Try the sling carrier and see how much of a difference it can make to your sanity and her comfort

Good luck!