In PHP there are a lot of variables that I should check. Is it the same on Go?
This has nothing to do with Go (or PHP for that matter). It just depends on what the client, proxy, load-balancer, or server is sending. Get the one you need depending on your environment.
http.Request.RemoteAddr
contains the remote IP address. It may or may not be your actual client.
And is the request case sensitive? for example x-forwarded-for is the same as X-Forwarded-For and X-FORWARDED-FOR? (from req.Header.Get("X-FORWARDED-FOR"))
No, why not try it yourself? http://play.golang.org/p/YMf_UBvDsH