I agree with the other ladies that it's very unlikely but not impossible. Is there something happening with your body that makes you think you might have conceived? Was it a typical AF? If I were you, I'd take a home pregnancy test once enough time had passed just to set my mind at ease one way or the other and not do anything that might be harmful to a child in the meantime, just in case. I agree with them about the visit to your Dr. too, even if a HPT is negative. If you are having the symptoms but aren't pregnant, perhaps your hormones are acting up a bit and a Dr. will get to the bottom of it for you. Best of luck to you!
Second what Adgal said...if you ovulate four days before your period it's pretty difficult to even implant a fertilized egg. Spotting four days after sex *could be implantation bleeding. It's a little early...but I had implantation six days after ovulation. So, who knows? Also, you don't say if the bleeding you're referring to as your period was at your regular monthly cycle time...so it's just hard to say what it could really be. If you're not sure, call your MD!
Well, it is possible to ovulate 4 days before your period, but typically you need at least 10 days between ovulation and period in order for the egg to properly implant. So if you are ovulating 4 days prior to your period that will make it difficult. However, you can see an RE who can probably help.
As for having your period when you are pregnant, you don't actually have a period. What you can have is some bleeding, although typically it will be lighter and more like spotting. Some women have had bleeding heavy enough that they thought it was their period though, and all turned out fine.
If you are in doubt, see your Dr. Bloodwork can clear things up for you. Good luck.