Getting thru TSA while pumping

I have to take an overnight work trip next week and need advice on air travel while pumping. Baby will be staying home, so I’ll need to bag milk and keep it cold until I get back home. I plan to bring:

1. spectra
2. spectra charger
3. large cooler bag
4. milk storage bags

How do I get thru TSA with milk? It won’t be frozen. And how do I keep the milk cold? Thanks in advance!