Issues with an over supply and newborn

My baby is 5 days old and my milk came in on day 3. My breasts become so swollen or engorged its painful, that I hand expressed a lot of it. Between hand expressing and using the pump just to relieve the pain and pressure I think I ended up with an over supply and baby is showing signs of its negativity like coughing during feedings, gassy, burpy.. etc.

I really would like to get this supply down because even after she eats my breasts start to hurt an hour or so later. What should I do?? I don't want to end up with clogged ducts or mastitis and that's why I kept expressing the milk out, now I have a stupid amount for a 5 day old baby.

I'm a first time mom

Thanks in advance.