Congrats you're pregnant!!!!!! Of course it can show up right before AF is due! In fact some tests can tell up to six days before a missed period so you were definitely in the normal timerange too get a bfp. Congrats again : )
Quoting AustinsMommyX:" Can a pregnancy test show up positive if you're about to start your period? Today is my due date for ... [snip!] ... all symptoms of my period but not yet, and I just took a test today out of curious and it showed positive. Now i'm wondering..."
It's VERY unlikley to have a false positive unless you are on some sort of medication to my understanding. (A specific medication that I'm not sure of.)