Would it be possible for someone to develop phimosis in your late teens?

Yes: There are a variety of skin conditions or infections that can cause phimosis at any age.The failure to easy retract the foreskin over the glans in normal in newborns but should resolve in childhood.

Possibly if ...: Recurrent inflammation of foreskin/glans penis - balanoposthitis may slowly cicatrize the opening of foreskin to eventually become not retractable. Such a process may take years and even decades to be fully developed. Besides, without a direct look, it's hard to reach an accurate Dx for most reasonable Rx. So, see urologist for clear assessment timely.