Breast milk storage question

Hi! I am a new mom with a 1 week old! Breastfeeding so fat has been going really well! I’ve decided to start using a Haakaa on the opposite breast I’m feeding from just to catch the let down and start storing it for later use. I know the guidelines for how long you can store BM in the fridge/freezer and all that but because the let down is only a small amount and not a full feeding worth, can I store the milk in a BM bag in the fridge, catch more on the next feeding and just add it to the first bag in the fridge until the end of the day? Then I’ll freeze the entire bag from that day. I’m just wondering if the bag is refrigerated, can I add new milk to it from the same day?? Any help on this would be great!