Very attractive snake & very nice set-up, though you'll want to fill the space in the large hides with substrate so he feels secure there.
Sounds like he has an RI...clicking & mouth-breathing is not normal or a good sign. With good care he may recover on his own, if not see a vet. Don't wait too long.
By "good care" I mean proper temps. (what are they? corn snakes prefer "room temperature" about 72-76*, with a warm area of 85-86*), & no handling (minimize
his stress) If he's staying in the cold part of his cage, it may be because you've over-heated it...corns require much lower temps. than BPs. Keep his humidity up a
little (if it's dry where you live?).
I keep his warm side at 80-85. Humidity is usually 30-40%. Thanks for the advice!