Pumping milk and adding it to bottle in fridge?

Katie • 20 years old, FTM to baby boy Kaden Chance 💞👶🏻☺️
I'm a FTM and just got my milk in. I have only a tiny bit in a bottle in the fridge. Can I pump some more and add it into that same container that has the fridge milk? Or do I need to use a different bottle to store? 
My breasts are engorged and hurt. I don't want to use a bottle yet so I thought I could save the milk for a later time.