Yes, It is possible to get pregnant at any point in your cycle however in order to get pregnant, you must be ovulating. Essentially, it remains possible that you may ovulate at any point in your cycle therefore you may get pregnant at any point in your cycle. Normally, you will ovulate on day 14 in a 28 day cycle. The likelihood that you are pregnant is very small but not impossible. I think you are fine. I suggest that you remain calm and on the first day of your missed period (assuming that you do miss your period) take a home pregnancy test.
White discharge is completely normal. Wait till the day u are due and if you don't get it then test that morning but I don't think you were ovulating the day after your period. That seems a little soon and if there is no ovulation then there is no pregnancy. Good luck.