Pick me up could mean to be choosen for a particular purpose.
"Pick me up for this team."
" - Who wants to take part in this play?"
"- Please pick me up as I love acting"
Pick me up could be to give a lift/ride or to someone.
" PLEASE, pick me up at 10 pm so we can go together to the ball.
Or it could be to go somewhere with (someone) as a companion or escort by picking them up.
Pick me up later so we can stroll a little and talk a bit