I just finished beating the mission where you race Lamar, and you have to return the car to the mechanic. I pulled out my phone and tried the quick save feature an it made this weird noise. I didn't know what it was so I quit the game because I had to leave. I come back about 3 hours later and my game isn't saved not even in load game so I have to ply all the missions all over again! Help please!
You can't quick save while on a mission, sadly. You'll have to wait for the mission to end (you get a little summary screen and are generally asked to press A/X to continue) before you can use the phone to quick save.
I've also been in a state before where I couldn't use the quick save feature even though I was pretty sure I'd finished any active missions. In that case, sometimes killing myself reset things. Other times that didn't work and I had to load my last autosave instead.