First day of last period was August 20th and I had sex with an ex boyfriend on Aug 28th and I am pregnant and do not want it to be from that day August 28th so is it possible that I got pregnant from that day?

Yes, it is possible. However, dating conception is not an exact science, and even knowing exactly when you ovulated will only narrow down the options for you. If you were with more than one person during that time, then there is no way to definitively eliminate one of them but a DNA test.