I used to be pretty shy, and I'm still a quasi-introvert (but some people would never guess- it really is situational). My best friend in 6th-8th grade was extremely introverted, she really didn't talk to anyone and it took her a while to warm up to me. I guess she wasn't really my best friend until 7th grade- it took us all of 6th grade to get to know each other.
I don't think there is anything wrong with being the "quiet" one, as long as you are able to speak up to get your needs met, and as long as you are able to form relationships with other people. You don't need to be friends with the whole world, but it makes life much better to have one or two people you can talk to. And I don't think they need to be in gymnastics with you necessarily, but if you are spending a lot of time there and those are the people you have the most in common with, then it would be good to make a friend there.
I have been in situations where I felt so different from the people around me that I closed up and couldn't talk to anyone. Looking back I do think that made things worse, but I recognize how hard it was at the time. The first time I was in a situation where I related to the majority of people it was so amazing- finally I felt free to be myself! I have spent my life seeking out those kinds of places where I feel comfortable, and over time it seems like those kinds of places have expanded for me. It has gotten to the point where if I land somewhere and I get that "alien on a strange planet" feeling and I don't know what to say to anyone I find it so unexpectedly strange, and I get a little nostalgic! I don't know if that is because I have gotten better at relating to people or if I have just done a good job of finding the places I like. It all started with going to a gifted HS, and then finding my tribe in college and beyond. I still feel out of sorts in some places.. and some of those places I still go to because I like the activity, even if I don't really connect with the people.
I hope this perspective helps you see how things will change over time, and how you will change too. You can change things at gymnastics by talking to people, but even if you don't you will someday find people to be comfortable with. Probably. Even my old best friend is a lot more outgoing than she used to be- for her it took joining a band and working in the music industry for a while. She connects with artists, which I definitely am not- but we had complementary temperaments when we were kids.