YABU, these things work out.
My dd1 was born on 6/2. Ds was due on 13/2 (2 years on). So, as dd1 was early, it was always going to be close, really.
He turned up early, late on 3/2 (10 days early - reckon it's the only time he'll ever be on time!!) and missed my Dad's birthday by a whisker. I'd joked "ha ha if he's born on Dad's birthday I'll give him Dad's name" even though we'd agreed a first name (original) and middle name (dh's Grandfather). So we stuck my Dad's name in too - ds loves all the "hey look at all my names!" stuff (he's 11).
So my dad, who always thought his birthday was unique in our family, ended up being bracketed by 2 grandchildren - now have family birthdays on 3/2, 4/2, 6/2.
And it's great. It's fun. We do joint cakes if we visit. My dad sees it as a great thing that 2 of his grand kids (almost) share his birthday. But in our family it's kind of a tradition - our wedding anniversary is my step mums birthday (and she's my real mum in spirit), my brother got married on my sills birthday - there are more!
Sharing birthdays is ok (even now when dd1 is coming up 14, ds coming up 11). Dd2 (10 this month) is actually cross that her birthday doesn't match with anyone!!
And you know what - no one cares