Worth paying out of pocket for another CT Contrast scan of aortic area?

I was sent to the ER in February and diagnosed with Kommerel Diverticulum and a right circumflex aorta after a contrast CT Scan. I guess the more serious problem of the two is the KD, but I read that chances are extremely low having both of these situations.

They acted like it was medically urgent but wanted to send me a hospital 90 minutes away at 3am in the morning and I'd have nobody who would know where I was.

I was sent home and referred to my state's top doctor for aortic surgery.

I coughed up two things today one of which happened before a virtual visit with my doctor. My doctor said he doubted the first thing was responsible for the throat problems and said he couldn't do anything more until I had my visit with the aortic doctor.

Then tonight, I coughed up some mucus and other trapped stuff that would measure about the same length as the measurements that were on the KD charts.

Now that that's happened, it's making me wonder if I should just pay out of pocket cash for another contrast scan so that way I'm not taking up time at a top institute that could be used for someone else (plus I need all on six dental implants and KD surgery would delay that by a long time)

Given what happened tonight with the swallowing back up and that I feel fine for the most part, would it be worth it getting another CT Scan?

I doubt my doctor wants another appointment before I see the aortic guy, so trying to figure out the best path forward.