Your period coming back has a lot more to do with your breastfeeding than it does with what method of delivery you had. Regardless of whether you had a vaginal delivery or C-section, the return of your periods has to do with hormones, and if you breast feed, it's much longer.
I think you should check your post-op instructions. I'll bet they say to wait for your 6 week check-up before having intercourse. What do you mean, "Why is it important to check with doctor?" Because you had major surgery! Major, invasive surgery with an incision in your uterus and in the abdominal wall.
You'll know it's your period when you have several of them on a schedule.
Meantime, every single women's health book out there will tell you to assume that you are fertile at all times, and you must use reliable contraception. Talk to your doctor immediately about your plans for a reliable birth control method based on your medical history and family history, and get on it when it's medically acceptable. Tell your partner that you are a new mom and he can wait the full 6-8 weeks if he loves you and doesn't want you to have complications. And please tell yourself that you are worthy of being a whole and complete woman with a good health profile, and that your baby is entitled to a mother (and in fact, 2 parents) who are smart enough to make much more educated sexual and health decisions than this one. Get a book such as "Our Bodies, Ourselves" so you stop using terms like "cummed" and "full intercourse" and stop doing things that cause pain and increase bleeding. A good book (well reviewed by women's organizations, for example) and a frank discussion with your physician or a great counselor at Planned Parenthood will help you learn about postpartum bleeding, resumption of ovulation, fertility and much more. Take your partner with you - he needs to learn more too. No well-informed man would ever dream of having intercourse with a woman he loved so soon out of surgery.