Time for some reasonable thoughts on this.
The winds reported on the EWR METARS during this time frame last evening were all under 10 knots.
Military drones do not fly in the national airspace around NY without FAA approval.
There is no way a military drone would be around Teterboro, in Class B, without the FAA knowing about it.
Reports of passengers "spotting" drones within a few hundred feet at 38000' "somewhere over Chicago" are also not possible.
The claim that a "green" pilot was too frightened to land at Newark and invented this is just plain crazy.
Again, the view from the cockpit is completely different from a passenger seat, and you see a lot of different things. You can easily spot other airplanes at 20 miles at night, and 10 during the day.
Drones/balloons etc., are not that hard to see if you are looking in the right direction and they are moving.
I have no idea what was in the Teterboro vicinity at 3500' last evening, but I do know that the uninformed speculation in this thread is not close to accurate.