I have never heard of a vet trying to drain a tongue, especially from an allergic reaction. If it’s possible, I can certainly understand the reason he would want to. Since the tongue actually originates in the throat, a swollen tongue can be very dangerous/life threatening. That’s a tough one. If my dog was having difficulty breathing, I would have them do everything as quick as they can, shot, tongue draining, you name it. But if the dog was not in any kind of distress, I would have had him give the shot, knowing that he could do the other later, if needed.
I bet you’re pulling your hair out trying to figure out what the devil they could have gotten into. One of my GSDs used to all of a sudden break out in hives and get shocky. We never did figure out what caused it. I used to have to keep an epipen for her. I did learn to not go out of a particular door at work that seemed to have something to do with her episodes. I don’t know if it was a bush, a bug, or a chemical, but it sure was scary. I’ll be praying for your pups.
