I really didn't like feeding from my right breast in the beginning, it was uncomfortable to hold and it hurt, a lot.
But what happened is the milk in the breast got infected - called mastitis. My breast got very hard and hot. I ran hot water on my breast in the shower to help loosen it up and had to pump (often). My midwives had herbs and compresses and some other solutions - I am sorry I don't have those here to share. But really each person has a unique situation and I feel especially with this you should talk to someone directly.
Breastfeeding, as natural as it, takes a lot of work to get right. There are lactation consultants who have the information you need and of course there is La Leche League which is free. As well as your pediatrician.
You didn't mention that your left breast hurt, just that it is more comfortable. Just in case I wanted to say, remember the baby has to LEARN to breastfeed just as much as you do. If the latch isn't correct you HAVE TO STOP break the latch and try again, even if it 10 times or more. If the baby latches wrong your nipple will become increasingly sore - oh it goes on and on....good news is that when it's right it is easy and wonderful (also it gets easier - way easier for both of you through time).
Congratulations and good luck!
L