it should be perfectly okay for you to lift weights at the age of 16. But the fact that you are hurting is an indication that something is not right. My guess is that it is the amount of weight and the way your are lifting, probably a combination of both.
If you can, getting a professional trainer for just a few sessions would be ideal. The trainer could show you the correct techniques and put a routine together for you that is balanced and appropriate.
In the meantime: it it hurts beyond normal muscle soreness, lay off and let things rest.
I wish you good luck.