I can also step it up wardrobe wise. I'm a grad student in the sciences in Northern California so anything but jeans really wouldn't work, but I can wear my more fitted pairs with darker wash for work and meetings, and sub out my sneakers and tees for more "real shoes" and button downs.
Back when I was a grad student (in Southern California, in the social sciences) and a TA, I was still often mistaken for a 16-year-old when I was in my mid-20s. A mentor suggested to me that I would have more authority in the classroom if I dressed more formally on teaching days. (At the time, I sometimes had a problem being taken seriously by some of the students.) While my fellow grad students were in jeans and t-shirts, I wore skirts and heels and always made sure to do my makeup. Although I stood out, soon my fellow grad students understood that I dressed up on teaching days. It also made a big difference in the way the students treated me.
Good luck. And believe me, in ten years you'll appreciate looking ten years younger a lot more than you do now.
When I was a TA, I did this, too. Jeans and sneakers and my hair down for non-teaching days; skirts and heels and a bun for teaching days. This has the added bonus of making you completely unrecognizable to your students, so they don't bug you with questions if they should come across you in the library.
Maybe it would help if, instead of thinking "I need to look older," you focus on "I need to look more authoritative." Because you don't need to be older, you need people to take you more seriously.
Really, what are you going to wear to work at a grill? Jeans and a braid are perfect for that. So maybe work on the things PPs have suggested, your tone of voice, your body language. Even evaluate your vocabulary. Do you ask for things, or do you make statements? Do you defer when someone interrupts you when you are talking, or do you plow right over the interrupter? There's lots of little, subtle clues we all have that give other people an impression of us.
For a while in grad school, I had a full-time job at the university library, at the Circulation/Reserve Desk as the Evening Supervisor. I was in charge of 20-30 student workers and was the only staff person there for 6 hours a day. I always dressed nicely, in large part because of the baby-face thing. I had a reputation of being able to deal with the toughest patrons.
Then one Saturday, I had to run in to take care of a few things that hadn't gotten done during the week. I was wearing jeans, my hair was in a braid. One of the student workers came and asked me to help out with a patron. She knew I wasn't on duty, but the guy was really hassling her. I couldn't give him what he wanted, because the book he wanted was checked out. He got madder and madder and finally burst out, "I want to see the supervisor!" The look on his face when I calmly replied, "I am the supervisor," was priceless.
But I never had that sort of problem when I was dressed in more authoritative clothes, nice slacks, a button-down shirt, a jacket.