it's normal, your body is getting the "milk sacks" ready for when you really lactate. you'll start getting real full about 3 days after you give birth. by those nursing pads to stick inside your bra, or use paper towels or toilet paper, just fold it into a square to make it comfortable, you can even cut a maxi pad in half .
My Breasts started leaking colostrum at 20 weeks(all 4 pregnancies). It's normal! Just your body getting ready for breast feeding. If you don't plan on breast feeding, I suggest you wear a REALLY tight bra post partum( think 4 sizes too small sports bra). Or just talk to your doctor about what you can do. But for now, just invest in breast pads. Lansinoh makes some GREAT disposable, leak-proof ones.
You begin producing colostrum in your second trimester, and anytime after that your breasts may begin to leak. My last pregnancy I started leaking around 28 weeks, this time I was only maybe 17 weeks along when it started.