Rose is the only modern companion who was a teenager, wasn't she? And even then, she was 19 in the first season (though Billie Piper was older).
Going through the other modern companions, Jack certainly wasn't a teenager. Mickey was five years older than Rose (per Father's Day) so certainly not a teenager. Pretty certain Martha was said to be in her twenties or so, and Donna definitely was not a teenager.
Amy and Rory were nineteen in The Eleventh Hour but were twenty-one in the rest of their first season. River's certainly not a teenager, Clara was said to be twenty-seven or so in Deep Breath. Bill was in her twenties, while Nardole was not a teenager.
Ryan and Yaz were 19 in their first season. Ryan explicitly said he was in his first season, while Yaz is implied to be given the two of the went to school together. Granted, that raises the issue of how many 19 year old police officers are there already working without supervision. Graham and Dan definitely were not teenagers.