Hello there,
I agree with opus88's comments. Also even though your kitty wants to go outside doesn't mean you have to let him outside. There are all kinds of dangers outside for a cat. Also as your cat only had the procedure done yesterday, I would keep him inside for observation. As Opus88 suggested, if you have concerns about your cat, for example, the very fast breathing.
I wish you and your kitty well. Eve ( mother of Sammy the cat )
You really need to discuss your concerns with the Vet clinic....there is no charge to call even after hours and take to a Vet esp about the breathing, that is a genuine concern
Good luck, keep us posted okay