Cord-like Feeling Running Along Crease After Breast Augmentation?

If I understand you correctly you have a cord running paralled and NOT perpendicular to your breast fold.. This is either your incompletely release inframammary fpld or the remnants of your pectoralis muscle cuff along the costal margin subsequent to release of the costal margin origins ofthe pectoraliz major muscle 

What you are describing is not uncommon at all. I would discuss it with your surgeon next time you see him so that he can examine you just to be sure since we can't examine you over the internet. However it's not uncommon to feel lumps and bands under the skin while you are healing. Most of these things will go away over the next several months, and sometimes may even take up to a year.

Bands such as yours are often inflammation that will resolve.  Normal inflammation associated with healing actually is most prevalent at about 6 weeks postoperatively, and with what is called remodeling of the tissue, your problem will likely resolve in the next few months.