that seems a really good idea to me too. A bite can seem so trivial at first, especially if it's like this and not an attack by an angry cat. I was bitten early in the morning and just went 'ow' and forgot about it, kept feeding Swampy etc and only washed it about 10 mins later. I give Swampy so many pills and often he's caught me a little bit, but I did recognise at the time that this one was a bit more painful so his toofies must have gone in deeper. Plus he was on abx so I wasn't that worried and it is a small puncture wound. When I went to the surgery they tried to fob me off with the nurse too and didn't prioritise my appointment, so don't assume that the medical surgery receptionists are 100% on the ball on this one either. I am sure they are at A&E though. Mind you, here you could go to A&E and only be seen hours later. So I need or needed to know what a real emergency is, as I can't leave Swampy for 5 - 6 hours to go there unless it's essential.
The GP went on about my tetanus status too, which (hopefully!) isn't that relevant in an indoor cat as I can't be re-immunised. I had a bad reaction/over-reaction to that vaccine so the docs at the time told me any wound, get antibiotics. (not amoxyc but never mind!).
I think everyone could use more info as the feeling unwell after a bite thing isn't immediate is it. (I read on the web that the best abx is metro-something too btw). I know the internet's not infallible, but that's where I also read about peroxide killing bacteria in non bleeding wounds. The vet nurse says she uses hibiscrub if and when she gets bitten or scratched and she's never had an infection.