Ay mama, totally normal yan at maraming babies ang ganyan, lalo na sa first month when they're still learning to feed! Pero since sobrang dami ng spit-up mo baby at kailangan palitan ng damit all day, I'd really suggest checking with your pedia just to make sure walang reflux or feeding issue na need attention, pero hindi ka mag-aalala, most likely okay lang yan at kailangan lang ng time para ma-adjust ang system ng baby.
In the meantime, try burping in the middle of the feed din, not just after, at hold baby upright for a bit after feeding para ma-settle ang milk. You're doing amazing ah, these early weeks are so challenging and you're already so attentive sa baby mo, that's the best thing na kailangan nya ngayon, a mama who cares this much!