Stress-hit Draper vomits on court after win at Australian Open
The 22-year-old was on court for three hours 20 minutes in searing heat during the hottest part of the day and needed a medical timeout to have his blood pressure taken at one point.
He also suffered severe abdominal cramping before eventually coming through 6-4, 3-6, 4-6, 6-0, 6-2, urging Giron to hurry for the handshake before he threw up.
"I kind of felt bad because I obviously just beat the guy, and I was saying, 'I need to shake your hand, mate, but I need to get to that bin'," said Draper.
He attributed his problems to anxiety and stress in pressure situations.
"For me, it feels like my breathing starts to really struggle, and I can't get the oxygen in me," he said.
"You are not only playing the guy, you are almost competing against yourself because you're not obviously feeling 100 per cent.
"That's something I'm going to have to speak to someone about and try and sort of figure out methods in those situations - because it will happen again for sure - to try to calm me down."
He added that having his blood pressure taken mid-match was because his chest felt tight.
"It (pain) was referring to my back, and I just felt I couldn't really hold myself up. I think that's what stress does to you," he said, adding that similar situations had occurred before.
"Always first round you feel a little bit more out of breath. It's obviously because of the tension. I think that's most players. I had it in Miami when I collapsed a few years ago.
"Obviously that shows the improvement that I'm able to kind of take more suffering and deal with it (now)."
Draper will face American 14th seed Tommy Paul in the second round.