Check out this website:
Plenty of information there about blossom end rot & prevention.
The ones displaying symptoms should be culled and tossed into the compost. In my experience, it clears itself up after two or three sets of fruit: the roots have developed more by that time to take up additional calcium and overcome water fluctuations.
The eggshells do in fact help; but not immediently - you are "feeding the soil, not the plant"
Later generations of tomato plants in the future will be less likely to develop the same problem.