I’m getting conflicting info online…I could use some real life info from others

Do I HAVE to wash and sterilize my pump after every use? Or can I just pop it in a baggy in the fridge and use it again? Example if I pumped at 12 and put the pump in the fridge and then pumped again at 3 and then washed it in the morning when we get up for the day?

As well as bottles. Do I have to sterilize the bottle every time or just the nipple?

Basically my problem is I have A LOT of milk and a very fast let down. My baby chokes and gags and then gets mad and sucks in a bunch of air while eating. He spits up a lot, more than what I think is normal. At times it’s soaking his clothes even if I try to burp him good or keep him upright after feeding. He will also fill up on formilk and then be ravenous again because he didn’t get the fatty milk at the end and then is super eager and has a hard time latching at first at the next feed because he 1. Has gas from all the air he took in and couldn’t get out the last feed. And 2. He didn’t get that fatty milk.

So anyways I’m considering just pumping off the first half of my milk and letting him eat the second “half” first at my breast and then giving him a bottle of what I pumped off if he’s still hungry OR just strictly bottle feeding him.

This is so frustrating for me because I really am struggling mentally with breast feeding and I feel so guilty because even though I have a lot of milk it seems like I’m not doing things right with all the puking he’s doing and the gas pains 😖

(Side note, he takes bottle and breast well and nipple confusion doesn’t seem to be an issue. He is 4 weeks old on Monday)