Edit: Sorry, I was looking under the version for Fallout GotY instead of Skyrim. It seems my version for Skyrim is up to date, officially, at least to what's available on Steam.

If you right-click on the game in your steam library, go to "Properties" -> "Updates" -> "Make sure this game is always up to date". If that's already set, make sure you're not running Steam in offline mode - need to be online to get updates. If you are online, go to the "Local Files" tab & hit "Verify Integrity of Game Cache" - that should download anything you're missing, including the latest patch.

It should of updated automatically for you. Did you restart Steam or https://support.steampowered.com/kb_article.php?ref=2037-QEUH-3335