1. Your body doesn't finish growing until 19-25 years of age. Does she want you to wait this long to start lifting?
2. Maybe you can print some of these and show them to your Mom (if she is swayed by evidence...). You know your Mom, so you can decide which ones, if any, to use.
Olympic Weightlifting - QWA - Information for Parents
Shows how weightlifting and weight training is undertaken by kids and is radically safer than other sports kids participate in
Kids? Weight Training Programs: Guidelines for Building Strength
WebMD article tells parents kids can start strength training at age 7 or 8 (actually younger is safe too, but I'm assuming you're at least 7...?)
The Benefits of Weight Training for Kids - NYTimes.com
researchers found that, almost without exception, children and adolescents benefited from weight training. Plus, its safe.
Olympic Weightlifting and the Young Athlete
Kids doing Olympic weightlifting. Helps build bone mass, not "stop the growth plates"
3. Lift at school or at a friend's house
4. Get into wrestling or football. The coach will make sure you're lfiting.
5. Do bodyweight exercises and get strong as hell...sooner or later, you'll get the weights
Bodyweight Strength Training Beast Skills
RossTraining.com - Full Throttle Conditioning
Bodybuilding.com - Combat Conditioning: Five Months Without Weights!