If you played while online, I imagine it remembers all of that stuff. If you delete your local save it may simply delete your progress in the career and tournaments. If you're lucky, starting a new game will wipe leaderboards but I doubt it. Copy your local save to USB for backup and try it.
What happened, a so-called friend thought it would be funny to post better times on your tag?
My cousin started a game on my main Live profile on my Xbox so I started one on my second profile. But now he got the game for himself and started his own on his Xbox ,so I was trying to delete the progress he made on mine and start over so I don't have to switch profiles everytime I want to play.
Also we can't play online together because my other profiIe I started my game on doesn't have Gold.
I looked in the memory on the Xbox and it only has the tracks I downloaded. No save game or anything.