Usually there is an emergency line that if you ring your normal vet no they will put you through to .

Have to say bad eyes ,sore throat makes me think of cat flu,has cat had its jabs?

The only thing I try to get poorly ones to eat is chicken,and use a dropper to get fluids into them,but I would definitely get vet advice on this one as cat has gone lethargic and thats not good .
Hope this helps a little