It's a real concern these days, isn't it? Don't worry, though. You can take as much milk as seems resonable for your time in the airports. They will scan it with a spectro annalysis "gun" but they will not leave it out of the ice chest long, will wear fresh gloves when touching your milk containers, will not rub it down for explosives and will not ask you to drink or feed it to your baby in front of them. If you get there REALLY early, they may ask how long your flights and lay overs are (I was at the airport 4 hours early once because of layover changes and the need to get out of the airport for real food!).
Unfortunately, very few airports have nursing mother's rooms, but you can use your breast pump in the bathrooms. One flight asked me to not use the bathroom in back, but the one up front, and on another flight I couldn't get through the bathroom's lines so just used the hand pump in my seat with a cover. It wasn't comfortable, but after waiting so long I really needed to and the bathrooms weren't available. Of course, I dump all the milk expressed on planes and in bathrooms because of the lack of boiling water to clean equipment between pumping. (The flight attendants did offer the tea water, but I didn't feel the pump was really clean after using it).
Good luck on your trip and take care!