I echo the sentiments above.
At the end of your day your mom is just in 'protective' mode and is operating under things that were spoken as if they were truth when she was a kid. What she is saying is nothing new. In fact, it's old as dirt.
I would state most of us on this forum got our first Sears cement weight set when we were between the ages of 10-12 and have all turned out ok. I would never blame my being vertically challenged on weight training. It's just the cards I was dealt.
IRT your protein intake, my kids have been drinking protein shakes fairly regularly since they were young and they both drink a shake a day now. It's just part of what they do. My 14 yo daughter is now as tall as I am, and I am confident my son will tower over me one day (not that that's much of an accomplishment).
Most of the damage I did to my body I did at your age because I was a dumbass and overtrained big time Early on we got most of our programming from Muscle and Fiction so I was doing Albert Beckles bicep routine with my spindly ass rope arms and Lee Labrada's chest routine at a time in my life when if I turned sideways, I disappeared.
The advantage you have is the wealth of training resources available to you. The challenge you have is sorting it out and not jumping from program to program like a spastic meth head.
Not to mention, most of us old guys would give away something dear to us to have your endogenous levels of T.