Let me clear something up, you have two Ocellaris Clownfish in your tank. They are the same species with different color morphs.
There are a couple scenarios:
1 - They are both immature Clownfish and they are sparring for dominance.
No worries here. One will win dominance and become the female of the pair.
2 - They are two females.
This is the worst of all cases. If they are both female they will fight to the death. This is where your LFS failed you. It doesn't matter how long the first one was in the tank, if they are both female they will never get along until one is dead unless you have a rather large tank.
3 - Your original Clownfish was female and the new Black & White has not yet changed gender.
This is what I think is happening. The female will quickly assert her dominance over the new Clownfish and they will bond. There is a slight chance that she will reject the new fish but that is uncommon for Ocellaris.