My Usually Very Happy, Energetic Shitzu Has Occasional Spells Where She Makes Long Snorting Sounds That Almost Sound Like She's Choking Or Having Trouble Breathing. She Trembles And Seems To Be In Distress. This Happens Even After She's Fallen Asleep, Why?

This sounds like what my dachshund does. She is now 11 years old so I'm used to it, but I did take her to the vet when she was young for it, as it scared me to death.  He called it a reverse sneeze, and said it was nothing to worry about. I just pet her and tell her she's ok and she finally stops. But if you think it might be something different you should have your vet check it out. One way is to record it, like on your phone so your vet can hear it if she won't do it at his office for him or her, whatever your vet is. I know it sounds scary, but if it's the same thing it's nothing that will affect her future in any way, just sounds like they are going to stop breathing. If you go to "PAW-RESCUE.ORG"  and put in "reverse sneeze" you will find a lot of info on this, if indeed this is what your little one has. I hope it's the same thing, and hope this helps in some way.

My dog does this too and recently--he's nearly 9--in the past six months it has turned into episodes of his being unable to get through the thick mucous and he stops breathing. I put my finger down his throat to try to pull the mucous out. It is the consistency of conditioner. When it's bad, I put him on antihistamine/steroid but have no idea what this is, and the vet doesn't seem to either.

You could be describing a reverse sneeze if so simply place a finger over her nostrils if it is a reverse sneeze it will stop immediately.  However she could be having a seizure so she really needs to be seen by a vet.

We had the same thing, what we did was rub her neck and throat area and she stopped after 30 secs or so.