alright. ty-lee and airbending. let's talk about it.
Has she told anyone? Not... really. Mai would definitely be the first to know, but for a long long time this is something she entirely keeps secret and tries to just ignore because it freaks her out and confuses her. but she can't ask anyone in the fire nation, if she does it draws suspicion, and what would happen to her if they did find out? this is why I like to headcanon she left to be in the circus instead, besides a few other reasons that remain canon to the show.
It troubles her. it raises a ton of questions that she's afraid to gain answers to. ignoring and pretending like it's not a thing is the easiest way to cope. she only really knows how to utilize it for her insane agility and light feet. to most people, they would see her movement as that of a circus acrobat's. to someone more experienced, however, something might seem a little familiar.
Even after the fall of the fire lord and joining the kyoshi warriors for a time, ty-lee keeps it to herself. you go that long denying these things, you tend not to think about it. But things change when she visits republic city for the first time. seeing so many different nations mixing and mingling, has her feeling some type of way.
Eventually, upon returning home to the fire nation capital, she confides in Mai about it. after a lot of coaxing from her best friend, she eventually works up the courage to seek out the Avatar to hopefully gain some insight into this unexpected ability.
Being completely detached from her airbending roots, ty-lee isn't sure just how much of her heritage she actually wants to reconnect with. she is curious and wants to know how it came to be, but she doesn't see herself dedicating her life the same way the air acolytes do, nor is she sure she'd want the ceremonial tattoos should she ever gain mastery over the element. ironically though, she is still kind of a nomad in her own way.