I didn't have the same issues - but wanted to share a similar story. I had thrush with my first child and our experience was very painful. Bite a washcloth, curl the toes painful. But I was so determined to prove the NiCu doc wrong, who'd sent me home with a bag filled plump with formula, the entire staff chuckling at my attempts to hand off colostrum ('he needs way more than this to survive' they'd said). So I kept at it, 'round the clock. Painful nursing after painful nursing. It eventually turned into the most natural moments for the two of us - . Our daughter was the same, multiplied. She latched so tightly that her face would scrunch up. My toes were curled before we even got into the position to nurse. And the thrush was so severe my nipple was bleeding and, well, a deep carved groove threatened to eventually pull that one off. Seriously. I also grabbed onto every lactation consultant I could find to discover how to rid us of the thrush, keep the milk flowing - and uncurl the toes. It was the gal that had me feeding her steadily on that side that prevailed. She said the milk would heal the wound. She felt different posititioning would balance the suction, etc. Who knows, but she instilled a confidence in me that said - yes, i can.
I now believe it was a lot of things that kept us going, formula free. But the biggest was to nurse through the pain OR pump through it. I know of moms who nursed solely on one side. That works, too. And of moms that tandem nursed babies. I think it comes down to you, your body and what you are learning about feeding your baby. I would say to start with one side or the other, switch midway - and then go back. If starting with your 'good side', she'll have some in her tummy and won't be as frantic - will be in the nursing mode, try the other to keep the milk coming - and switch back to empty the other side out OR try the opposite, giving her the frantic suction on your sore side to get the milk moving and switch to your other side to fill her tummy. And then after... I'd set up shop to pump both sides empty. Yup, probably painful, but I'd keep that milk flowing for a few days to see if it doesn't get better.
Elasticity. We laughed at my third baby. She managed to twist, pull, turn, etc - with me painfree. It does come along :)
Best wishes, hang in there - and let us know what happens :)