I give most of my own vaccines as well. If it doesn't say West Nile or WNV on the package, it doesn't have it. Sounds like, from the label you read, that she gave a standard 5 way, but not WNV. You can buy WNV separately and it is around $20-$30. But the 5 way combo doesn't have it unless specifically stated on the label (Prestige V + WNV is the one I use). I only started doing my own vaccines because we (me and my horse) travel a lot and boosting is cheaper on my own than a vet visit, but I go to the vet once a year and have the shots given by him so I can have a complete health record if I need it. IF you are already going to the vet, it really isn't THAT much more expensive to have him do it. It only gets expensive if you are making a trip for *just* non rabies vaccines.
Since you probably have to get a rabies update, and you have to do that at the vet, you can bring the box to show the vet and ask for WNV when you are there. And it is good to get a Coggins with your name on it as the owner.