Problem with cats eye, not getting in carrier to see vet.

Hi everyone, this morning my cat came to my room and had a watery eye that he was keeping closed. It was mildly red and he was rubbing it now and then.
I called the vet to book an appointment and got one for half an hour later however he is refusing to get into the cage and growling and getting upset when I try to put him in the cage so now we have missed the appointment. I’ve rescheduled for Monday evening for the next available appointment.
I’m anxious and not too sure what to do. Please can someone advise me.
He is a 5 year old outdoor cat and was completely fine up until this morning. I’m worried if there is something in his eye or if he’s scratched it.
He’s up to date with all his vaccines.

He knows that we’re trying to get him in the cage now so he’s on guard and refusing to come near anyone and is hiding under sofas.

All advice is much appreciated