Hi,
My LO is the same, she is such a content little baby most of the time but not when she's tired. She'll go to anyone quite happily, but if she is tired she will scream until she is handed over to me. She's my first baby and breast fed so not sure if this has added to her clingyness?
Things are getting better though, she has only recently started going to her her daddy without crying too, and we did this by sort of letting her cry it out. I couldn't bear it at first, which is why I think she cries for me, because if she's with anyone else and she starts crying I usually take her back straight away to stop her crying. I thought it'd never work but it only took one go of letting her cry with her daddy with me by her side saying sshhhh and after 15 minutes she was fine and has been since. I tried it yesterday with her nana, doing the same thing, she started getting tired and crying while on her nanas knee, she was looking at me for comfort so rather than taking her frome her nana I just kept saying shhhh and again after a few minutes she settled and went to sleep on her. This is a major improvement for us!
I think letting her see that I'm ok with her being comforted by someone else has given her reassurance to let other people hold her while she's upset. Hope this makes sense?
Every baby is different but hope you find something that works for you too. I love me LO, but it was getting me down a bit that I wasn't even able to leave her with her daddy without her screaming for me. I didn't realise how much guilt comes with being a parent (so worth it though)!
Good luck x