Can someone copyright a photograph they took of me that I gave no permission for
Yes. In fact, copyright is automatically awarded to the photographer. They don't have to claim or apply for it.
The reason this is the case is that copyright protects the artistic work, in this case a photograph. Copyright is not designed to protect a person's likeness (or that of anything you might photograph), though there are various other laws that may apply to those things.
... and use it in a smear campaign
The smear campaign may or may not be considered libel. But if so, it would be unrelated to copyright - the copyright belongs to the photographer and there is no question about that. If you wanted to take action against them for their smear campaign it'd have to be one related to libel, not copyright.
Note that for something to be libel, it needs to provably do more than just show you in a bad light or be a bad photo.
and have me take down a picture of ME while "critiquing" it (fair use!).
Knowing that the image copyright belongs to the photographer in this case should help you with your understanding here.
If you have copied the photo without permission from the photographer, then this is an infringing copy under copyright. You may indeed reasonably believe that your use of the photo is "fair use", and you may be correct. The only way that would be officially determined is if the photographer took legal action against you and it made it to court, then they would decide if it is fair use or not.
If the photographer has sent a DCMA takedown request to your ISP or similar party, then what this means is if they take it down now, they will be immune to certain further legal action (they may have been immune anyway, but complying with the takedown would guarantee this). It doesn't mean they are obliged to take it down, but unless they care a lot about you, and believe that the image is non-infringing because it's fair use, they probably should. It's up to the ISP.
If the photographer has sent you a DCMA takedown, then it's up to you to decide how to react and whether to react at all. You are not legally bound to comply. If you believe your usage is "fair use" then you may well choose not to. Either the photographer will give up and leave you alone, or will decide to take legal action. If you don't comply and, hypothetically, the photographer goes on to take legal action against you, that's the point at which you stop taking advice from people on the internet and get your advice from a proper lawyer, because at that point - if it does get to that point, and it rarely does - what you say to the photographer may influence whether you can win and how much damage it will do to your bank balance. If on the other hand you do comply, it will almost certainly be the end of the matter.