John seems like kind of a jerk. You expressed your concerns politely, asked if you could come to some resolution, and he flat out refused to be an adult. Then, you solved the problem on your own, without requiring any change on his behalf, and now he's relentlessly teasing you?? Ugh. This guy needs to grow up.
I do think that complaining about the teasing would not look great to management. I think you should tease him right back.
Him: "Oh, so how's our little prima donna today?"
You: "Great, space invader, how are you?"
His kind of teasing is just being mean with a smile. No reason you can't fight fire with fire. He sounds like the kind of person who exploits weakness. You can quietly show him that you won't be cowed by his teasing.