Line fault at the outlet -- do I need an electrician?

I would not open the panel if you dont have to. You've gotten a lot of good advice here. Like mentioned above, I would shut off the breaker to the circuit, then open up the closest receptacle to the panel that would be reversed polarity.  If you fix that one, then every other box will be fixed. Highly unlikely it is reversed inside the panel. 

2 tips. Be conscious of any switches outlets when testing, so there are no surprises.
When trying to find the first receptacle box, you can disconnect one pair of wires from the receptacle. THEN reapply power to find out if you're in the beginning or middle of the circuit. OR a more safe way is to test for continuity from one box to the next WITH THE POWER OFF. Then you'll know which is first. 
I also would not open a light fixture for starters. I say this only because of your experience.. It may very well be in a light fixture feeding the first receptacle box. So the first box may look correctly wired, but the connection from the fixture may have been reversed. This last scenario is my best guess.
Good luck
Yes, please update if you can. Curious...
Thank you

"@ cissado

Good post except in the case of where the duplex receptacle device may have been used as a junction for the make up of neutral and Hot conductors coming in and going out of the outlet box."

I'm not sure what this means exactly. Maybe because I wasn't clear in my post. I usually am not clear... it's my bad writing skills.
I just meant the first receptacle may have been fed from a light fixture. Also, that the wiring inside the light fixture box could be wrong. 

If it was a diy, and I were to guess which of the two boxes is wired wrong, my guess  would have been the light fixture. 

Personally, I wouldn't take down the light first, either. I would guess the first receptacle, possibly disconnect... and go from there. OP shouldn't even do more than that. Give it a quick try and see if it works. Then of course call a pro. 
I'm just bored. I don't post here this much.
Good luck

Yes, it's usually the first one that needs fixing which fixes the next in line.
I would get that plugin tester for the rest if the house anyway and make your job easier.
Good luck

Oh, I misread. You just need to reverse one, then the next one in line will be fixed.

Hopefully you fix the last receptacle in the circuit, otherwise you'll have to change out the rest because they'll now be reversed. 
Well, it seems you've done it. Congrats.