I think your daughter is getting old enough that she can understand Mommy has a hurt. Right? I mean when she hurts herself does she come to you crying, does she understand, do you kiss her boo boo, reverse this, you have the hurt and she needs to help? So, you can try to explain as best you can that she needs to be your little helper, and that you can't hold her much or rock her to sleep. Replace you with a stuffed animal or a doll. If she doesn't have a favorite item, then maybe go and have one made, make it special, explain to her that this is the "thing" that you will sleep with and hold on to in place of mommy because she is hurt.
I deal with a terrible back, gave birth to 10lb, 11lb, and 8 lb little boys, so they started out big, and didn't help the back much and by 16 mths you can only imagine how big they were. I had a flare up once, my body went numb and I fell down 6 steps when I was pregnant with the second one, and my son was only 17months, it scared him, but you know what he did? He got his favorite bear and blanket and gave it to me to make me feel better, they understand, they really do. He sat with me for awhile and then I needed him to go get the neighbor and he was even able to understand to go across the street and get my friend, (that was a scary thing to have to do) but he did it. Children are smart and I sense that you both have spent plenty of time with her and she probably would do just fine, if you talk to her like she is a big girl.
As far as wanting the closeness you can deal with that by having your daughter cuddle with you on the couch where you don't have to lift her, use stools so that she can get up by herself, and tell her how happy you are that she is such a big girl and helping you so. When it is time for her nap, you take the stool and put it by her bed, and have her crawl in, again praising her on how much she is helping mommy feel better. She might not like it, but again if you have bought her something special to use to help her, she will get it.
You really need to make her understand how much pain you are in, she will get it. But you need to be consistant. Don't pick her up during the day and walk around with her, make sure to remind her that you can't pick her up because you are hurt, it works, she will get it.
Good luck to you.