I published my mission successfully. Thats what the email says. But When I search for it Ican't find it. Is there a period of time before i can find it in the search and acually play it myself?

Try hitting the 'stop reviewing' button, and then 'start reviewing' again. Search for it.

additionally, you have to be a reviewer in the first place if you want to see it right away. It won't show up for the general public until it's been reviewed a couple times.