Push ups won't affect your height. But a hard gym work can do
it. When the body still grows, this is possible thanks to the
clefts which are on each end of the bones. The bones get longer
this way. When the body stops to grows, these clefts "close"
themselves. When lifting heavy weights, the weight can press on
these clefts and close them and the bones can't grow. Thus
affecting the height.
Guys who still grow should only lift weights and work with weights
which are not more then the growing bones can bear.