Do I have to keep a creeper whenever I draw cards in Fluxx, even if I was drawing cards to give to other players for "Everybody Gets 1"?
After reading the rules carefully, I found that this is mentioned in the Creeper section:


  Note that this is true any time you draw a card; for example, with 'Everybody Gets 1' you must keep all Creepers you get while drawing the cards you'll be giving to other players.


If you drew Creepers during Everybody Gets 1, you would keep the Creepers you got, draw new cards to replace them, and give 1 non-creeper to each other player. After some searching I found it on the mailing list for Looney Labs. :)