I can't get the free alistar skin

Just submit a Player Support Ticket letting them know that you wish to receive the Unchained Alistar skin and the wonderful Blitzcrank Bot should have that done for you in a jiffy

Blitzcrank Bot is an automated system Riot added to their tickets to look through them and pick out key words or phrases to allow him to handle certain specific actions that don't necessarily require a rioter/staff to help with and allows him to do it automatically, the Alistar skin being one example since the youtube thing doesn't work right and people can't get him normally like that, so it will pick up the words and perform its function to add it to your account.

If you're interested, you can learn a bit more Here