Help me with my muscle growth! 10 points!!!?

okay so i am a vegetarian. i can not eat fish, turkey, eggs and meat. i can drink milk. and eat vegetables obviously. i am skinny and i have been going to the gym for weeks. i lift 20 pounds (10 in each hand) like 40 times. i do that everyday at the gym, as well as machines. i do that for an hour. now my brother, who is skinnier than me is still stronger than me. he never goes to the gym and sits around on the laptop all day. me, i dont look or feel different, but yet my brother can still beat me in an arm wrestle. PLEASE HELP THIS MAKES NO SENSE TO ME. ( i think my brother hit puberty if that makes a difference)?