I had this Headcanon pop into my head earlier when I went to get my shots.

So Finny's a lab experiment. And he doesn't seem like he'd really like more needles stuck in him. Imagine every time he has to get a shot, he has to have his fellow servants and Ciel in the room to feel face, then one of them has to hold his hand, which he probably squeezes with a death grip, with his eyes shut tightly. Then afterwards when he goes home everyone just snuggles him to make him feel better.