Am I reaching here or have I discovered a clue as to Childs being the thing?

You can read it that way, but I have two issues with this interpretation:

1. You ask if "this was Carpenter's way of subtly implying..." - well, in the commentary, both Carpeneter and Russell say that the ending is deliberately ambiguous. Their intent is unmistakably of creating vagueness as to who is who. Russell at one point says he believes MacReady to be human, but then Carpenter says that he still might be a Thing... so ambiguity is the intent of the creators here. Russell is leaning towards Mac being human, and I myself think it makes no sense for him to blow up the Blair-thing if he is the thing. There is no other hints of direct infighting between the Things in the movie anyways.

2. In-universe - suppose you are right - but how would Mac know in universe for sure that Childs is a Thing? What clues him in? Can you support it with anything - other than the fact that Childs was off to the side for quite a while and anything could have happened - but that doesn't prove it one way or the other. We are privy to all the information MacReady has, and that's not much. So if he only offers drinks to Things (which is in itself a stretch, since he offered his drink to Blair in the shed in a moment when Blair was - almost certainly - human), what makes him so sure Childs is one? You need to fill in this gap first, before we can evaluate your theory.

Isn't that just a fan theory because you can see Kurt Russell's breath at the end but not Childs? It's likely that's just a continuity error.

You do realize there is no correct answer to this question, right? John Carpenter himself said he left the end ambiguous and let the viewer come to their own conclusion. For over forty years, people have been speculating on this when the answer is, there is no right answer. It is a choose your own ending kind of deal.

The real question is: where the fuck is Nauls? He might still be alive, he might be a thing.

What was Childs drinking?

When MacReady last saw Fuchs in his laboratory, Fuchs was so nervous that he grabbed a beaker containing a chemical that was obviously so lethal that it could be used as a projectile. MacReady was perceptive about this since he came into the lab to see if Fuchs had devised a way to defeat the thing. Perhaps, after Fuchs died, MacReady found a way to put it into a bottle so as to trick a thing into drinking it.