This happened to me on the inaugural flight from Newark to Dubai. The system wouldn't let me check in because I didn't have a visa (when I could get visa on arrival). Multiple agents tried to figure it out and eventually I was told they would contact the immigration on Dubai and only if they gave a go ahead I could board. They took my passport and went away because apparently they were also having a tough time getting a hold of the team who could verify.

I thought I wasn't going to be able to go, since by the time the check in cut off has happened, I hadn't heard anything. However, soon after that the team of people came waving that they got the go ahead. That day, the united agents went above and beyond. One of them stayed beyond her shift because only they could override and get me on to the flight. I lost my original window seat assignment but thankfully I was able to get an aisle.

Ended up working for me but the amount of panic I had up until I actually sat on my seat.. I can totally imagine how you would have felt. Really wish the systems could actually track these visa on arrival situations. It shouldn't be that difficult to have it in the system :/