I had sex August 29 & 30,2014 and was ejaculated in both days, had my period September 5th-8th, I had blood tinged discharge September 22nd and 23rd, spotting the 24th and blood tinged discharge the 25th. My next period was due October 3, 2014 but I didn't start. What could be the reasoning?

No reason, many reasons, there is no way to know and tell, without exam and something women just are late, or they miss a period.

Next it is just Oct 4th, so one day late, is not even really late. So, just wait a few days.
Of course pregnancy could be possible, but not as likely.

You can try a pregnancy test now, although it is a little early to test, but do it, first thing in the morning. When you first get up.

If the test is negative then wait two week, and if still no period, test again.