You were 6 days late and you have just started your period can you be pregnant?
I doubt it. Being late for your period is actually quite normal. Getting your period to soon is also quite normal. There has never been a single time in my entire life that I could pinpoint when I was going to get my period. I have even got my period twice in the same month. Now that's a bummer. Talk to a doctor and get regular exams so this way you & the doctor can figure out what your personal normal & abnormals are because every one is different. No two woman are alike.