He could just be trying to adapt to the new smells and the new place.
Or the stress could be giving him a small respiratory infection. It's hard to say though with no other symptoms right off the bat, but lethargy and keeping the head raised can be suspicious.
Has he been making clicking noises when held? Yawning more or having a bit of drool around his lips?
You know your noodle best! So if these seem way out of place, it is definitely worth keeping an eye on. I know one of mine personally sits with half her body out and propped on top of her hide when she's ready for a meal. But if my shyest male did? I would be suspicious too!
Vet visit seems like a good choice, but it may also be a bit to early for some of the other symptoms. And starting them on meds too early can sometimes be more stressful than waiting it out. It could be worth seeing what they think and having them a phone call away for if the other symptoms DO start showing up rather than fighting to have him seen if he does worsen