Hello and thank you for using JustAnswer, my name is ***** ***** I will be helping you with your question today.
I think your first actions are the correct ones to change the hotmail password ***** a precaution. What I believe this email to be is either a prank email or an email showing that the senders account has been compromised rather than your own. I would also suggest changing the password ***** your google accounts from a different computer than the chromebook. Since this is a chromebook there is no need for antivirus locally on the machine. Give the chromebook a restart and you should be good to go.