I have a sick cat that won't eat hasn't use the litter and walking slowly. Can I make a appointment to get her checked?

Take her there. They'll take care.

How about giving her up? Where should I go?

You have to a vet.you can find low cost.on the internet.in your area But try the SPCA

I would call ahead they are always busy. Especially with cats. They should be able to treat it there.