In a dispute it is possible for each opponent correctly to attribute a fallacy to the other. Not in the example above, in which A and B merely make statements and do not present any arguments. Your dialogue is not a case of argument but of claim and counter-claim. For a fallacy you need an argument - reasoning from premises to a conclusion.
If Raj is silent then Raj is not talking (premise).
Raj is silent (premise).
Therefore Raj is not talking (conclusion).
This is an argument but there is no fallacy in it.
Suppose, however, the following dialogue, about product X :
That brand of medicine, X, has been on sale for decades.
This brand of medicine, Y, is new.
Given the advance of science, Y must be better than X.
Fallacy : novelty does not prove superiority.
My grandfather has always taken X.
It always clears his illness.
Given that record, X must be better than Y.
Fallacy : irrelevant evidence - grandfather's experience with X tells you nothing about the quality of Y, which he has never taken.
In this dispute, the arguments on both sides are fallacious. So B can point out A's fallacy, and A can point out B's fallacy.
I have set out the respective arguments informally but there is no harm in this for present purposes.