I went through the exact situation and I was also 37 when we conceived. I knew my dates were correct (I also write everything down and track my mucus as well) in terms of when my husband and I were together and when I ovulated. The dates the doctors gave me were just under two weeks off of my original ovulation date. However, when I looked back at my charts and noted what I wrote down, what the doctors said made sense. I think I ovulated twice that month...the type of mucus I had proved it, but I assumed I was safe because I already ovulated two weeks prior!
Don't you know, I conceived 6 days before my period! I just ovulated for about 1 day at the end of the month and thought it wasn't possible. To this day, I think this: I was 37 and the body can start to do some weird things every now-and-again. I guess it was just one of those times!
Our baby was never underdeveloped in utereo or at birth. She is our 4th baby and she was the smallest (by 5 oz). She still is! She is 14 months old and about 20 lbs, where my other kids were 18 pounds at 6 months! But she is doing great developmentally, socially, and physically. She is extremely observant and bright. She is just tiny. So we lovingly call her our "Peanut."
So don't stress out! A relaxed mommy is better for a developing baby than a stressed mommy. Enjoy the ride!