Gulping down milk

My son seems to GULP down milk when breast feeding, to the point it will cause him to cough. He doesn’t have this issue if bottle fed - which I was told was the opposite (that he should drink quicker from bottles).

Is there any way to fix this? I feel bad and am almost considering being exclusively a pumping mom - which is NOT what I wanted...

He’s only a week old, he’s my first baby, so I’m just figuring out this parenting thing and it breaks my heart to be the one causing him to gasp and cough.