One of my DD was like this, she even cried when I put her down to go to the loo. She wanted to sit on my lap or be carried all the time . I coudl only shower when she was asleep.. Sigh . I know it's very wearing and you sound as if you are coping well .
However DD wasn't placed at birth and she did grow out of it and by 3 she was able to go to nursery for a few hours a week . As a teenager , she is able to go on school residential trips .
She is still quite attached to me and texts and phones me when she's at school . She doesn't like me going out in the evening etc .
For some reason, it's much worse for her when I go away from home ( which I do two weekends a year ! ) but she is fine to go away herself. I think it's because she hold this mental image of " home " with me in it.
However she is able to lead a totally normal teenage life And overall her issues are very minor , she is one of the easiest ( or least damaged /traumatised ) of all our children .
But I'm not sure if that helps you with your DD now. Given that you have experience of " normal " clingy children, does this feel different to you? If so, I think it's worth getting some specialist input now.
I'm wondering if you DD was exposed to drugs in utero ? I've heard that this can be one manifestation of the brain damage it causes