Pumped milk at work shelf life

Sravya

So.. I pump at work.. keep the bottles in an insulated cooler bag that also has ice pack in it. I come home usually after 2.5 hours after I pump. I know it stays good for 6 hours.. but my question is after I come home, can I keep it in the fridge? How long can it stay good in the fridge?

Or if I keep it in the same cooler bag after coming home also, how long will the milk stay good? TIA