Bring him to a CAV, certified avian vet, even if he WASN’T sneezing! You want them to do a full workup on him or her...and if you want, a sex test. Be prepared to spend about $400 without the sex/DNA test, but you just gotta do the full health workup.
Mealys can be incredibly mellow, and since you just got him today, of COURSE he’s going to be a little skittish, or VERY skittish. You gotta give him a few weeks to adjust. Don’t rush him to do this or that, but if he’s letting you pet him, you’re halfway home! He’s going to be great!
I would even leave the cage closed a few days. Let him learn its security. Maybe sit by the open door a little, but don’t make any moves he doesn’t like. Let him make the moves.