Sorry to hear about your cat. Nursing a beloved pet through their last time can be hard. It can also be a precious time.
I hope you do give your vet a call. There's no need to be scared - if the vet suggests you take the cat in you are not in any way compelled to. You do not *have* to do what the vet says. The vet may have good advice to offer, with or without moving kitty.

As for what you are 'supposed' to do... make him as comfortable as you can. Love him. That's all.