Jaclyn, I now run my giveaways on my website, I have a tab on my facebook page which links to it. That way I can let everyone know I am having a giveaway and to click on my facebook tab to enter.
The Tab has a 'gateway' which means people must 'like' as they enter - that way you still get likes.
You can't notify the winner on facebook, it must be via email, and then with they're permission, you can announce who the winner was on facebook.
Facebook don't even warn you about it - they just shut your page down! It has happened to so many people, even pages that had 900 and more fans!
I am running a giveaway at the moment - it gets drawn tomorrow - your welcome to have a look at the way I set mine up.
https://www.facebook.com/TRaewyn then to the 'competitions and giveaways' tab. (It takes you to my website).
Hope this all helps!