Can't wait to see pictures! Good idea on the nutrical. It may just be that she likes to be held, but it is certainly not worth the pain and agony if it isn't the case. Are you letting her get adequate napping? I liked to let my baby sleep in a little collapsable house when he was just a little baby until he would wake up, then I'd let him out to go potty, then play until he slowed down, and then put him back into his house. That way he got familiar with his little house and we were able to monitor his food intake/outake and his energy level. It was hard to get him on a schedule but now he is an awesome little poochy who plays all morning and then sleeps the afternoon away. I wish I could have his lifestyle!
I also forgot she was 16 months, maybe she just likes to feel safe, you know? I'm sure she'll come out of her little shell, but maybe she just needs some extra love and patience from you. Try letting her sleep for a while and when she wakes up be energetic and invite her to come play with you and her toys. After enough times of your invitations, I'm sure she'll take a leap and come play with her mama. Just a thought.