When I was 13, I had a random "Aha!" moment. I had been wearing boyish shorts. I don't remember what kind but anyway, I had noticed just then that the men around me did not wear shorts at all. They always wore pants. From then on, I adopted a more conservative way of dressing and ended up always being asked if I was in college. Now I'm actually college age and get asked if I've graduated or working on it. Hah. Far from it, but a useful assumption.
So. To look older, start dressing like men and not boys. Lose the t-shirts and shorts, wear the dark slacks and button-ups. I think wearing long sleeves with the sleeves rolled up looks better than just short sleeve button ups, but you should watch the professional men around you for hints. The way you type also is a dead give away, not to be mean.
(For the record, I did start wearing shorts again about eight years later. Just the slacks kind and not the jersey shorts, and when appropriate.)