for your purpose, no need to build own web site

got to webshots for free
http://www.webshots.com/, register an account, then you can build your online albums.

2. flickr.com:

if you have a yahoo email address, you can logon using your yahoo email ID and upload the photos.

3. pbase.com
it is another resource where you can build online albums.

To let your family in China see your child, you may install skype with a webcam available and make video calls.