How could I convince my mom to allow me to join the army?

This is a tough one for you. My only son joined the Marines when he was only 17 and I was a nervous wreck. But if your Mom truly loves you she will want you to pursue your dreams and aspirations. We didn't give birth to you so that you could take care of us the rest of your lives. You must find your own way in life. Don't let your Mom control you through the 'getting ill trick'. You will end up resenting her for it. Sit down with all the facts and tell her what your plan is. Be assertive and strong so that she can see that this is your dream. Then go for it. Just remember that all Mom's suffer separation anxiety when their kids leave the roost. Good Luck.