It is possible to have one breast letdown harder than the other, especially if it is engorged. In that case, expressing/pumping before nursing that side, may help. I would nurse the baby on the right on a nursing pillow and use the breastpump on the other breast while he eats- that will allow for an easier let down. You can then freeze that milk to have as emergency milk for later. And after the breast is softer, you can again try nursing the left. I would also try different positions on the left- like a football hold instead of a cradle, and see if that helps the problem.
Another possibility is to see a pediatric chiroprator (although most have at least worked on their own kids and can do some kids- if you live in a rural area, you can call and talk to the local ones and see if you feel good about them). If baby's neck is out of place from the birth, or positioning in utero-, it can lead to baby having a hard time turning his neck to one side to nurse, and thus causing him to have a poor latch on only one side.
I would not worry that baby isn't getting enough. Women nurse twins, so your body will make what he needs on the side he nurses from, as long as he seems healthy, I would not worry.
Congratulations! Those first few weeks of nursing can be very hard- you are doing a great job!