Is this your first pregnancy? If so, you have nothing to worry about, especially as long as you get your Rhogam shot at 28 weeks. I am RH- and had issues due to bleeding. The OB gave me the Rhogam shot to prevent any antibodies from forming, even though the chances of that are extremely slim. If you have any bleeding, make sure to tell your OB just to be safe.
The policy at my doctor's office (and I assume yours as well) is that if they see a mother is RH- they go ahead and check to see if you have formed any antibodies that could pose a problem. If your OB wasn't concerned, I assume they already knew you hadn't become sensitized yet, but it never hurts to ask!
My Grandma and Great-Grandma are both RH- and had 3 healthy pregnancies each with no miscarriages. And my Great-Grandma delivered before the shot was discovered! So don't worry too much. I understand how scary it may sound but chances are that everything will be fine.
Re: Has anyone had Rh negative complications?