Is competition wrong? That really depends on your concept of competing. How can we work out if there is something amiss with, say, competitive sports?
If we run through the fruit of the Spirit, that might help us form a picture: love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self-control.
My advice: if you can't picture each of these in the context of competition, then your concept of competition is wrong. Within sports, I think it would be hard (but not impossible) to find a sportsmanly attitude. After all, winning is the goal. That makes it hard for both the winner and the loser to be spiritual.
I tend to see collaboration as a more Spiritual form of competition. Racing to help others improve, and improving myself to be a better help to others. Thus, sport is about health and social connection for me. This is not really competition, but I do think it is a better garden for Spiritual development.