can my childs image be used without permission?

[Eric Lefebvre]

All those uses (being used on a Facebook page and website to promote the photographers work and entered into a competition) do not require a model release in most countries.

It’s not the picture, but how it is used that determines the need for a release. For instance, an image that is printed in a newspaper, shown in an exhibition or reproduced in a book might well be immune from a privacy suit. But the commercial sale of coffee mugs or t-shirts with the same image would probably not enjoy such protection. An advertisement almost certainly would not be immune.

Even if the images become the property of the contest owners, without a model release they are somewhat limited in how they can use the image. They can use them in an exhibit as art, for news reporting ... but they could not use the image of your child for an advert supporting a product or ideology.