Bottles at night time?

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Does anyone have any experience with giving baby bottle at night vs nursing. I’ve noticed at night I’m way more engorged and baby (3 weeks old) often chokes, coughs, gags through feedings. She only latches for a few mins and then is uninterested in relatching. She’s then super fussy and seems really gassy and an hour later, we repeat the routine. This seems to only be at night after her long stretch of sleep (4-4.5 hours) when I’m super full of milk. I end up having to express anyways because she only feeds from one side and the side she does feed from is still super full after. During the day we have no issues and she latches well for 20-30 mins, drains my breast, sleeps well after etc.

I’m wondering if just giving her a bottle of the milk I have to pump anyways would help? Obviously if she’s getting a bottle, she won’t be blasted by my letdown.