Watson was beaten 6-2 7-5 by the world No 165 but was severely hampered by illness as temperatures reached 29 degrees Celsius at Flushing Meadows.
She said afterwards her symptoms – sweating, back pain and feeling short of breath – were similar to those she experienced during a nasty bout of glandular fever in 2013.
Watson was diagnosed in March that year and did not play again until the French Open in May. “I feel similar, yeah,” she said.
The 24-year-old needed one of the tournament doctors to carry her bags as she gingerly walked from the court after the match.
Watson had called a medical time-out at the end of the first set, doubling over in discomfort on her chair, and was in tears as she underwent treatment.
“It was horrible to play. I was very ill,” Watson said.
“I’ve had a fever for the last three days but playing in this heat is almost impossible when you feel that bad.
“I was struggling to breathe and then my back, I don’t really know what it is, but I’ve been to see the doctor.
“I’m going to get some blood tests done and figure out what it was.”
Watson was a junior champion at the US Open in 2009 but she has now lost six consecutive first round matches in the senior event.
The world No 73 said she considered pulling out of the tournament on Monday night.
“I actually did think about it,” Watson said.
“But I’m not one to retire or pull out. It’s not in my nature. I thought I would try.
“It was really hard, obviously physically but also mentally not to think about it. Near the end of that second set I was trying to stand up let alone play.
“I don’t want to take anything away from my opponent, she played well and it was tough to play against me. She didn’t know what was going on.”
Watson enjoyed a slight revival following her time-out but spurned two points to clinch the second set as Hogenkamp claimed victory on her debut in the US Open main draw.
“I think the time helped my body to give it a bit of a rest,” Watson said. “But the pills they gave me and treatment didn’t really help.”
Watson must now decide whether to play in the women’s doubles later this week alongside Holland’s Michaella Krajicek.
They are due to face American pair Raquel Atawo and Abigail Spears in the first round.
Watson added: “I have to see what the results say but right now I’m still in the doubles so I’m going to try to do well there.”
Stockport’s Naomi Broady beat fellow Brit Laura Robson 6-7 (4-7) 6-3 6-4.
British men’s No 2 Dan Evans is through to the second round after beating American Rajeev Ram in four sets.
Evans had only once before gone past the first round at Flushing Meadows but he was a convincing winner on Court Four, beating Ram 6-2 4-6 7-5 6-1.
The 26-year-old joins compatriots Kyle Edmund, of Beverley, and Johanna Konta in round two, where he will face either Germany’s Daniel Brands or the talented Alexander Zverev.