I'm not a vet but I've had a variety of birds over many years and I'm sure that it's something in the throat area. I noticed in you new video that you have a full spray of millet in his cage, and although I also feed it, I just give a small ball of it and on the full spray, there are filaments that enclose the seed and as he digs into it while snacking, he may be swallowing some of this material and some of this may be catching in his throat. After your vet visit, you may want to try cutting back and eliminating the spray from his cage for a while. Just a hypothesis from my own experience and the circumstances.
He was making the sound before getting the millet. I gave him a full millet on his jungle gym yesterday and today (same one) to encourage him to eat and make the sound so I could video it. He normally only gets millet when I'm trying to convince him to eat something... I mix a few millet seeds with veggies and eggs sometimes. Oh, and he gets millet sprouts.
Unfortunately he stopped eating his sprouts (alfalfa) last night and only ate a few seeds this morning and none this afternoon. There aren't any seed shells at the bottom of his cage so I know he hasn't touched them.
He isn't interested in the millet anymore either. I swear he acts like he's choking! That is not his normal playing sound even though I know it may sound like that to someone that doesn't know him well.
His droppings have changed. They are very small. The last one was just 2 parts... a lot of the clear liquid and a very small amount of solid that was much lighter in color than his normal. There wasn't any "white cap" like usual. What does that mean?
I've noticed he's holding his wings down more than usual too but that could be because he has several new flight feathers coming in that he isn't used to? Or because it is ridiculously hot here. He is drinking water. I'm hoping the heat is the reason he's not wanting to eat. I'm feeding him seed on his mirror now one piece at a time. I got him to eat about 10 seeds.. Tomorrow cannot come soon enough. I'm so worried about him!
Ok right after I wrote that he had a BIG normal dropping.
Oh my gosh! I'm going crazy over here!!! I hope I go to the vet tomorrow and they tell me I'm crazy and nothing is wrong. How did I make it through raising three human children and I'm losing my mind with a little budgie?!