a sandwich isn't a problem. However, I don't know why it would be better to try and bring milk and/or yogurt. Both are readily available in the airport terminals, and flights have milk onboard, too.
Yogurt is one of those items that I'm honestly not sure if they'd try to call it a liquid or a solid.
Just for ease of it, I'd personally make a PB&J sandwich that can go without refrigeration and pass on the cooler packs, the milk, and the yogurt and buy those as I needed them instead.
Less hassle AND less junk to carry around.
I've brought baby formula through and stuff like that because those aren't readily available. The stuff that can be found anywhere, though, isn't worth the trouble IMO.