And despite his athletic accolades, which include being a nine-time All Star and being ranked third in NBA history with a career average of 9.9 assists per game, Paul tells CNBC Make It that he was anxious.

In the past year, NBA point guard Chris Paul has dealt with a lot of change. The star basketball player made the move from the Los Angeles Clippers to the Houston Rockets in June after a high-profile trade — he had to adapt to a new town and new teammates.

Houston Rockets Guard Chris Paul looks on before an NBA game between the Houston Rockets and the Los Angeles Clippers on February 28, 2018 at STAPLES Center in Los Angeles, CA.

"Everyone always thinks us athletes, we've always got it together. That's a lie," Paul says. "I was throwing up at [a] photo shoot.

"I was out there taking pictures," Paul continues, "and I was like, 'Give me a second.' Boom. I ran out, threw up. Boom. Came back and acted like I had just taken a phone call. [It was] just the anxiety of knowing that there was a change that was coming."

Paul was scared. "I had been living in L.A. for the past six years. The decision that I made was not only going to affect me, but my family, my kids, everybody around me. It was a big decision."

But Paul realized the best way to cope with change is to embrace it.

"Sometimes change is hard, but it can be good," Paul tells CNBC Make It. "What it does is, it brings a challenge.

"It's a challenge — and if you're competitive and you want to do something you've never done, you have to accept the challenge, and I think that's what has helped me thus far."

One challenge Paul faced was being drafted to a team that already had another star point guard, James Harden. Harden and Paul "are two of the most notoriously ball-dominant players in the league," noted The Ringer in October. But the transition has been a success: The Rockets won the first 15 games Paul played for them, the Los Angeles Times reported in January, and SB Nation dubbed Paul and Harden "dynamite together."