Electrical – Hard wiring light bulb socket onto whire/black wires — small shock when touching housing

I tried to wire up a light bulb housing (just the part with the socket for the bulb) by connecting the neutral (white) wire to the silver screw and the hot (black) wire to the brass screw.

I should also mention that this is coming off of a 3-prong outlet. The outlet is broken out into green (ground), black (hot), and white (neutral). I need all three prongs for a fan which is adjacent to the light (the fan has a grounded chassis), and figured I could tie in a light bulb as well (light socket has only two ports).

It works, but when I went to touch the housing of the light bulb I got a shock. It was not too bad, but bad enough that I feel it is unsafe to use as it currently is.

Did I somehow mix up my neutral and hot wires when connecting to the lamp socket?

EDIT

I just went and out measured with my voltmeter the hot and neutral wires with reference to the grounded chassis of the fan.

It doesn't look like I mixed up the wires. How can I be getting a shock from the light socket?

EDIT2

I just checked electrical continuity between the leads … apparently there is a short internally between neutral + hot. So I will be replacing the socket.

EDIT3

So, I removed the socket and tested it alone. There is no short. I guess the continuity checker sees the parallel fan (turned off) and since an off fan looks like a short circuit, beeps. But there is no short through the light socket.

I also touched the light socket again in the same place as before; I got no shock. I have no idea what caused it initially or why it is gone now…

I have included a picture of the setup. Let me know if there is something wrong with it.

Here is a picture to a very similar socket as the one I am using (mine is from an old lamp). I have the socket suspended with zip ties from a grounded metal chassis.