Collecting colostrum

Hey ladies, I was given syringes to start collecting colostrum. I’ve collected about 5 ml so far in about 30 minutes however I’m really confused on how to store it, it’s in the fridge now, however how long can I actually keep it in the fridge? Can I fill the whole syringe then freeze it? Or can I only keep it in the fridge for the whole day, keep adding then freeze at the end of the day?

I know it needs to be used within 24 hours once taken out of the freezer I’m just confused if I can keep it refrigerated more than a day and keep adding throughout the week