@leakid,
Please don't stress, it's just a fluke. My husband and my favorite cousin were both born on the 6th of March, same year as well. One of my great-aunts died in the same hospital on the same day my mother gave birth to my brother also in that hospital.
I won't say that you're foolish to be nervous, for 10 years straight we lost family members either at Christmas, Thanksgiving, Birthdays or Wedding anniversaries. We did approach those times with a little anxiety, and flinched if a phone rang late at night. But it was coincidence, unpleasant coincidence, but just a coincidence nothing more.
If you are anxious when those dates are approaching, try to do something that your Mom, sister and brother liked to do, be great if it could be something you all did together. My mother died in February 1995, the following Sept would be my Mom's birthday, I felt low and wasn't sure why but mentioned it during my doc appt. My Doc asked if there were any significant dates coming up, that's when I realized Mom's birthday was about 10 days away. My mother loved shoes, so on her Birthday, I shopped for shoes. It actually helped. I hope you find a way to make those dates comforting rather then something to dread. Good Luck.