Should I be worried about mondor's cord?

Hard to say without a photo or exam.  A Mondor's Cord is a clot in a vein.  It usually resolves with time.
It should not effect the result of the breast surgery. Always best to
let your board
certified plastic surgeon know what is going on with your recovery. 

This is a small clotted vein, usually occurs under the breast or on the outside.  It will usually go away on it's own but it can take a couple of months.  You can do warm compresses and ibuprofen or other NSAIDS for the discomfort.

Absolutely not. I see it my breast aug patients all the time. Apply heat. Take anti inflammatories (if OK with your surgeon) and don't worry. It goes away in time.