Pumping question

AEL1107

My little one was born a month early and was in NICU for 8 days. Between the c section and NICU stay my milk has been slow to come in. I am currently pumping and nursing to help stimulate more milk. I was told you don't need to clean the pumping pieces between each pumping session but could just put them in the fridge. I've been doing that with rinsing with hot water first. I was just told I don't even have to rinse the pieces since milk is good in the fridge but doesn't that break the rule of mixing fresh with cold milk? Sorry if this is a stupid question! Thanks in advance

ILMomma

I store my parts in the refrigerator at work then clean them at night.