Mettaton goes looking for Duchess, eventually. He isn't feeling any better about anything, but he looks better after retreating to his room for a while and changing into a new outfit. Looking good is the first step to feeling good, right? And this way at least the shattered mess containing his SOUL isn't showing.

He finds her out in the gardens. Still not his favourite place to be, but he doesn't care too much right now.

"There you are, darling!" He manages a smile, albeit a strained one. "...are you all right?"