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you never really know which particular strain it was

You do if they administer an RIDT and it gives a correct result.

Rapid influenza diagnostic tests (RIDTs) are screening tests for influenza virus infection.
RIDTs differ in some important respects:

Some can identify influenza A and B viruses and distinguish between them. Some can identify influenza A and B viruses but cannot distinguish between them. Some tests are waived from requirements under the Clinical Laboratory Improvement Amendments of 1988 (CLIA). Most tests can be used with a variety of specimen types (see Influenza Diagnostic Table), but the accuracy of the tests can vary based on the type of specimen collected (for example throat swab versus nasal swab).

I believe, but could be wrong, that a viral cell culture is required to distinguish subtypes.