Time of conception??

Ok so my LMP was September 2nd 2018. My cycle is normally between 33-35 days. Every detailed fertility window calculator said that my possible conception was between the 18th and 25th of September. Ovulation was about the 20th of September. I had sex on the 21st and 22nd of September and 14 days later on the 8th of October, I started spotting. So I took two tests on the 11th and 2 tests on the 12th and they were very faint. I took two more tests on the 15 as well as getting a blood test done by the doctor both showed a BFP. So, my actual question is, did I conceive on one if those 2 days? Because the math adds up that I did and if I was pregnant any time earlier, the tests wouldn't have been faint and I would have spotted earlier as well (I know that not every woman spots but for those who do, it's usually 10-14 days after conception)