i'll say C
the question asks which of the following MUST be true.
option B just presents one situation (it is possible) however option C says either they are fine or they have measles, both can't be true simultaneously

I will go with C as well.

I will go with B

One more C,
what's the OA?

OA is B

and here is the explaination

These two statements are called 'contraries.' That is, they cannot both be true, but they can both be false. The latter would valid if, for example, two of Shirley's children had measles and the third one was fine. But no combination of illness and health in Shirley's children will allow both Ellen and Lois's statements to be true. (C) is incorrect because there is no reason why either one of them has to be correct. Both Ellen and Lois could be wrong.

Why the explaination say "there is no reason why either one of them has to be correct" what is the critirion for this judgement

I was wrong with C
Answer should be B
Because the question is (Accepting the assumption that nobody who has measles is fine, which of the following must be true about this exchange? )

Ellen: All three of Shirley's children have the measles!

IF we consider Ellen statement to be true then Lois statement is wrong.

Lois: As a matter of fact, all three of Shirley's children are fine!

IF we consider Lois statement to be true then Ellen statement is wrong.

These statements were must be true if we take all three children. Then either statement can be true but when considering only 2 children than both could be wrong.

And we have to consider the option that must be true with the assumption that nobody who has measles is fine then in that case there is always a possibility that both could be wrong. And option never said both are wrong it is said that it is possible that both could be wrong. That's why this options will always be true..

Very different kind of a question
What's the source.