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Take a panty liner and cut it in half, use the sticky part on the inside of your bra and the liner part against your breasts. That should work pretty well.
I don't know what to do either I am only 21 weeks (I'm only 21, not as young as you but still clueless on this issue) and the same thing is going on with me but if I find any thing that works I'll be sure to tell you.
I'm a little late in replying to this, but if you are still looking for answers, here's a couple. The panty liner thing might work, so you could try that. Try wearing a padded bra if you have one. It doesn't stop anything, but it stops it from soaking through your shirt. You can also make fabric ones if you're crafty. Take some soft fabric (old t-shirts work!), cut out circles the size of a large mug, and sew them together (about 4 ply). Wear them in your bra. You can't stop it, but you can try to make it less messy. Especially since I imagine you're still in school, and that cannot be fun! Hope it works! (also, on a budget, washable ones are going to be way better then disposables. Plus, better for you nipples, and the planet!).