Because you said 'wainscoting' I assume that the tile you are describing is on the walls. The fact that this is your primary bathroom also leads me to assume a fair amount of traffic/usage. I have painted tiles and have never been happy with the long term look, they get scratched too easy and it looks like exactly what you have done... which is paint over tile. Installing wainscot with a proper top cap (some might call it chair rail ) and new baseboards would give you a great new look. The wainscot can be installed using a good construction adhesive.
I hope this helps, Jim
'Just a handyman trying to help'