my friend has a DD about 2 weeks younger than my DS & she's only just growing out of this now. until a couple of weeks ago, she'd scream everytime they visited someone's house (although didn't happen if they were at a shopping centre etc, just houses) and she'd have to be held until she went to sleep. she also wouldn't let anyone other than her mum & dad pick her up. she's only just letting her grandma pick her up & hold her now.

my DS used to do a similar thing when he was tired or a bit out of sorts - he still pretty much wants me when he's tired but is okay if he can't see me.

i don't know that there's anything you can do, just let it ride it's course & be as comforting & reassuring as you can so he gains confidence along the way