Let me see if I understand your situation. You are not breastfeeding but you pump and feed your DS from the bottle every 2 - 3 hrs exclusively? Wow that's really tough!
I think it's ok to give him a little bit of formula, but that would have the consequence of reducing your milk supply. Also, you may want to ask your pediatrician first and try just a little bit in the beginning to see how he's taking it. My DD had constipation when I gave her formula when she was 2 wks old. She also had gas pain a lot when she was on formula. It was a torture to see her in pain like that.
Pumping is really tough. Especially doing it that often. I had to do that the first 2 weeks of my DD's life. I had wash the equipment, sterilize them, and put the milk in the bottle (or plastic bag for later use), wash and sterilize the bottle afterward. Also, I had to mix formula on top of that. The toughest part is doing it in the middle of the night when I barely had any rest

.
Good luck to you!
LTW