「オリンピック競技」は英語で何て言う？

I started running a little over a month ago. Every time I put on my shoes...

× I feel like I'm in an Olympic game.
○ I feel like I'm in an Olympic event.

We say "the Olympic Games" when we are talking about the sum of all of the events. It's also important to remember that one sport might have several events, like tennis has singles and doubles, soccer has men's and women's, and so on. "Games" often have points, but not all of them do, particularly races.

× I may feel like an Olympic player when I put on my shoes, but...
○ I may feel like an Olympic athlete when I put on my shoes, but...

"Players" is generally used for participants in games with points. An athlete is someone "a trained to compete in sports or exercises", according to dictionary.com.

• athlete 【名】運動［スポーツ］選手、スポーツマン、スポーツ愛好家、競技者 (definition from Eijiro on the Web)

Like I was saying, the truth is far from my imagination. I watched part of the women's marathon. When I calculated their speeds and compared them with mine, it was clear that I have a lot of practice to do to get anywhere close. That gave me more admiration for the Olympians.

• Olympian オリンピック選手 (definition from Eijiro on the Web)
• admiration 【名】称賛、感心、感嘆 (definition from Eijiro on the Web)

I suppose I should use my running shoes tonight, then.