Any advise would be greatly appreciated!

My son is 10 days old. I started pumping at the hospital because he would fall asleep on my boob right away. Until now my reasoning was that I would breastfeed him once my milk supply was established. I realized that this way I am risking him still wanting the boob over the bottle by then so yesterday I started breastfeeding him. Boy was it a struggle! He seems to latch fine and at one feeding he was on the boob for two hours but was so fussy all day and still took a bottle after the breast (almost the regural feeding size)! When I pump I get the recommend amount of milk so I don't think my milk supply is an issue here. I just wish I knew why my boob is not enough for him after nursing for long periods of time. This is obviously stressing me out a lot so now I'm worried my milk supply will be affected by it but I don't want to give up on breastfeeding just yet. Any advise or tips you ladies may have would be greatly appreciated. Thank you!