I am installing a ceiling fan in my living room where there was no previous light or fan.

I ran the feed from an outlet to the switch box and ran the fan wire to the switch as well. I spliced the neutrals together and the blacks to the switch and the grounds to the switch. Everything is connected correctly. The issue is at the ceiling fan box... there is a constant neutral. Whether the switch is on or off, the neutral is always "on".

The outlets were hooked up correctly, meaning white to silver, black to brass. However, when I plugged in a tester, it said the hot and neutral were reversed. So I actually put the white wires on the brass screws on the recepticle and the black on the silver. Now it says the outlet is hooked up correctly (weird I know), but the ceiling fan box is still a constant neutral. I am am my wits end becuase I thought everything was hooked up correctly. Can anyone help me with this?

The outlet looks to be fed right from the circuit breaker, so I thought the issue might be there, but what are the chances of that being hooked up incorrectly at the breaker?

My guess is what you've done is screwed up a switch loop, a common mistake by people who just poke at the wiring without an understanding. Both the black and white wires going to the switch are HOT. The WHITE should have been connected to the BLACK wire from the panel and the black wire gone to the BRASS screw (often the tab on the receptacle device is broken out providing one switched and one non-switched receptacle).

No. I'm pretty sure I know what happened.

The feed TO the outlet is reversed. On the other end.

Originally he wired the light/fan CORRECTLY, but to an already-reversed feed. Neutral is not switched (nor is it supposed to be), but it was actually attached to hot, so his NC tester showed that the neutral was always 'live'.

Next he used the outlet tester and found that hot/neutral were reversed, so he swapped the wires on the back of the outlet. I'm guessing he swapped the incoming wires AND the ones that go off to the fan. Hence, the only thing he TRULY swapped was the outlet. The fan neutral is still connected to the wire originally assumed to be "neutral" (the white one feeding the outlet), and thus is still actually wired to hot.

The solution, Primo98, is going to be to make sure the fan wiring is exactly the way you originally described it (white conductor continuous/wirenutted from the outlet all the way to the fan, black wire interrupted by the switch, all grounds connected together), then figure out WHY the outlet is reversed. Wherever its power comes from (ie, another outlet), it may be reversed there.