According to the paramedic, he and two others performed CPR on the man for almost an hour during a flight from Orlando to Los Angeles last week.
The man reportedly began shaking then lost consciousness during the flight. Aldapa and two others "tag-teamed" doing chest compressions on the man.
Rather than performing mouth-to-mouth, a compressible oxygen bag attached to a mask was used to attempted to get the dying man to regain consciousness.
Aldapa says he spoke to the passenger's wife and she admitted that her husband was scheduled to get a coronavirus test done in LA after losing his sense of taste and smell.
The man reportedly told airline staff pre-boarding that he had no Covid symptoms.
"I spent the remainder of the flight covered in my own sweat and in that man's urine," Aldapa wrote.
The plan made an emergency landing in New Orleans and the man was taken to hospital, where he died a while later.
Speaking of his own Covid symptoms now, Aldapa told CBS LA he feels like he "got hit by a train".
"I had a cough, my whole body still hurt, I had a headache," he added.
United Airlines has said it is awaiting more information about what led to the man's death, after being initially informed he had suffered a cardiac arrest mid-flight.
"We are sharing requested information with the (CDC) so they can work with local health officials to conduct outreach to any customer the CDC believes may be at risk for possible exposure or infection," the airline said.