Breast milk oversupply?

Jennifer • Hopelessly in love with my soulmate, mother of three beautiful kiddos: ❤️03/03/08, 💙05/06/10 and 💙09/28/18

My milk came in at the hospital at just over 2 days pp. They were very engorged and my LO is not nursing enough to drain more than one side. I pumped the other side while he was eating twice today (our first day home 3 days pp) and got 2.5oz each time. I was worried because it is recommended he eat from each side for 10 minutes at each feeding but he instead feeds about 15 to 20 minutes on one side and that's it. Now that I know each of my breasts are producing 2.5oz+ I think he is getting more than enough from one side. My question is, if I keep pumping the opposite side at every 2nd feeding to relieve the engorgement, will this ultimately result in a huge oversupply?