
That is very possible, as dogs do not have the shoulders in a socket. What holds the shoulders to the body is muscle, which can easily be strained in a baby when picking them up incorectly.
If the pup is shy it will feel threatened by being picked up, and will probably be more inclined to growl at the children rather than the adults, as they are lower in the pecking order.
As another poster pointed out, never let the children pick thepup up. This time they may have done nothing to hurt the pup, but when you were not observing they may have been clumsy and caused the fear.
Four days is very soon for the pup to have leaqrnt to trust.
Thje children should not approach the puppy (good advice for any dog in future), they should crouch on their haunches and encourage pup to come to them, if it does not, then it is either tired or not confident enough. A treat held in the hand and a cheerful slightly exciting voice, and pup should be unable to resist. When pup does come to them, they should pet him gently under the chin alon back etc, but not on top of the head, which will obscur3e the vision.
Depending on how shy the pup is it may retreat (which should be allowed) or may relax enough to say roll over on it's back for a tickle. Rolling on back is also a submissive act, you can tell which it is by the tension the pup exhibits. If it is relaxed and happy then a quick rub.
Over the weeks as the confidence grows then he may need to be gently and firmly disciplined if he gets too confident and boisterous. It is a fine balanciong act, rewquiring more subtlety and maturity than the average child has.
Hopefully Fiona will post, who has small children and a young Cocker who had slight problems of this nature early on.