Awww the poor little darling, yes they are amazing. As is the things they can do.
He does sound fine now, but give him loads of love and effection to let him know he's fine.
He may love you even more after saving him.
Watch for swelling around the throat and cheeks.
I have seen a chin get caught in a chicken wire mesh a few years back.
One I had sold to a lady and told her chicken wire was no good but she didn't listen.
I sold her two and took them both back. Sad to say the one that got stuck passed away in my arms.
Her neck and cheeks became very swollen from the choking and she couldn't breath.
Doesn't sound like your little fur ball was stuck that tight.
You'll have do do something about that cage, and if your chin seems to be in any disstress at all get him to the vet. OK