Previous pump + fresh pump session??

So I’ve been trying to pump more often, and power pump occasionally to increase supply. But sometimes the amounts are less than stellar... less than a feeding sometimes.

So, my question is, as a first time mom, is: can you mix/store together a previous pump session with the current pump session? (I store my milk in reusable milk-storage bottles in the fridge... only full servings from the same pump session are frozen. So this question is really more for refrigerated storage). Or does the current pump session have to be chilled first before I can combine it with the previously refrigerated milk?