HFMD or his regular eczema flare up?

Hello everyone! My son is 1 1/2 and goes to daycare regularly. They do not have any cases of HMFD, but something’s weird is going on with my son.

He has bumps on his hands, elbows, chin, and legs. They are all like little patches where his prior dry patches are as well. He has been teething really bad for maybe about a week.

These are his normal dry spots for his eczema he’s always had it really bad on his hands and his dad accidentally put the wrong lotion on him this morning

He always gets that rash on his mouth when he is teething really bad and he is right now.

Although this is explanatory, does it seem too coincidental to be happening together?

The doctor cleared him and explained that the rash is a bad eczema flare up and his mouth rash is due to his teething. He was also cleared by 2 more doctors. Do you guys think they could be wrong?