Yes, your Golbat is shiny because it looks like the Golbat below.
If your Golbat looks like the Golbat below, it is not shiny.
Also, if your Golbat has a red star like the ones below, it is definitely shiny.
Shiny mark from Gen 4:
Shiny mark from Gen 5:
Shiny mark from Gen 6:
in generations before Gen 4, the shiny mark will not be a red star.
Shiny mark from Gen 2:
Shiny mark from Gen 3:
That was the simple part, now to find out if your Golbat has Pokerus.
Look at your Golbat's summary, if it has one of the below marks, your Pokemon has Pokerus.
Pokerus icon from Gen 3:
Pokerus icon from Gen 4 and Gen 5:
If your Pokemon has any of the below marks. Pokerus is cured, it still has the effect, it just wont spread.
Cured icon from Gen 2:
Cured icon from Gen 3:
Cured icon from Gen 4:
Cured icon from Gen 5 and gen 6:
If your Golbat does not have any of the Pokerus icons, try checking the other Pokemon that were in your party when the nurse at the Pokemon Center talked about Pokerus.
Hope this helps!