My first period after my c-section was heavy too, and long. I remember calling the doctor and asking questions because I was worried. After that cycle, they started returning to normal. If you get worried, call and ask your Dr. They're always willing to answer your questions. Your periods should get better after this one. =)
After my c-section, I went through the very same thing! It was awful - from what I understand, this is perfectly normal. It took a few cycles for things to return to "normal". It just takes a while for periods to resume some semblence of normalcy. About the nursing, it's always possible for periods to resume at any time. These kind of periods happened to me during nursing as well though I didn't get my period until about three months after the c-section.
Congratulations on your baby! - jen