To remount the filesystem as read-write from within recovery mode you can do
*note there is no space between remount and rw
mount -o remount,rw /
HOWEVER I can think of no good reason why your home dir ownership would spontaneously change so it sounds like you have other issues - maybe a failing disk? or your filesystem full or damaged?
Also DON'T do use the relative path '.' to change ownership in recovery mode - you won't be in your user home dir and it will screw up system permissions. If you still think you have an ownership problem you should do
chown -R you:you /home/you