It can be really rough. I felt like this as an older gymnast - I was a 13 y/o level 4, practicing with kids mostly age 7-10. I totally felt out of place, didn't really socialize with my teammates, felt weird about having gone through puberty already. The teammates taking up time and energy by not focusing was annoying, too. The thing is - and you probably know this as a rec coach - is that younger kids often just CAN'T focus and work hard the way you do. And some kids are probably doing gymnastics for fun and to play around with their friends, even though you're not. It can be lonely and stressful, and I'm sure you wish you had a supportive team environment.
For me the thing that helped was when I moved to optionals, I practiced with levels 7 through 10. So there were girls my age around, and everyone was usually working hard. I never made really good friends with anyone but I did feel less alone and more comfortable, and I was able to have fun with my teammates. It sounds like your gym doesn't have too many gymnasts, so there really isn't anyone your age around. In that case, it might be worth it to check out another one. Not necessarily to move - but if there isn't a difference in the coaching/equipment/opportunities, somewhere you feel more comfortable might be worth it.
I know focusing on your own gymnastics is important, but also having a supportive team can make the hard times so much easier. And it's also very frustrating if you're 16 and you're missing out on socializing because you're always at the gym and there are no peers on your team.