Did I make a mistake with this fluorescent light installation?
You shouldn't have any issue. Alot of ballasts are rated 120v/240v. A regular wall outlet is usually 15a 120v. Which you should be fine. Is this a t8 t5 or t12 fluorescent light fixture. I mean it is possible that you have a bad ballast that is only providing the proper power to the socket for only the bulb that lit. Try taking the bulb that is lit out of that side and switch it to the side that isn't lit. That should give you a rough idea that something is wrong. Check the connections at the socket of the side that isn't lit make sure the wires are actually in the socket. But again test the other side with the good bulb. sounds like a bad ballast in my opinion. But again no...plugging it in shouldn't have hurt anything. Getting power that way isn't really any different than hard wiring it.