Will a fracture on a growth plate (on the ankle) extend into nearby bone? doctor couldn't tell sprain vs. fracture on x-ray of ankle.

No, but. . .: The real problem is how badly if at all, the growth plate has been injured. This could change the rate of growth. At 16 you may not have too much growth left in the distal tibial. All you can do is watch at this point. I GUESS that you'll be OK.

Unfortunately: it is sometimes difficult or even impossible to tell. You should see a pediatric orthopedic surgery specialist to see if anything needs to be done to minimize long term damage.