milk storage/scenario

FTM: My husband and I went to dinner last night and I pumped prior to leaving.  My thought was, if he wakes up when we're at dinner, it would be easier to provide a bottle than try to BF at the table.  So I packed my milk in a thermal tote with a ice pack and we headed out. He ended up falling asleep on the way to the restaurant and he did not wake up while we were eating.  When I got home, I took the milk out of the thermal tote (the ice pack was still frozen) and put it in the fridge.  My question is, is it okay to put the milk back in the fridge after being in the thermal tote with an ice pack?  Do I have to use it the same day since I transferred it from the fridge, to thermal tote with ice pack, then back to fridge? 

I'm trying to get the hang of this pumping thing as I have to return to work in September and i'll need to pump.  Thanks for your help.