facebook privacy question!?

[dresdendrew]

I just made a facebook. I don't want anyone to be able to search me or anything. I made it so that no one can search me, but i don't want people to see that i have a facebook UNLESS i add them. I added people on facebook & now on their wall it says _____is now friends with Dresden. I don't want that to come up on their wall because then their friends can click me & see my wall & add me. Is there ANY way that i can make it so that i don't come up on their wall, & if i do, people who i am not friends with cannot see it? PLEASE HELP!
i did go onto my friends account who i am not friends with yet on facebook & went on to the friend that i am friends with's wall and clicked the notification on their wall that said ____is now friends with dresden, just to see if they would be able to see my wall, and they were. i blocked everything on my wall from people i don't know, but they still saw my wall. i just don't people to see me UNLESS i add them!!!