Actually,
Morwen spent more than 3 years, probably 4 to 5, looking for presumably BOTH
Turin &
Nienor, before finding their 'graves' at the same time as
Hurin did.
A timetable at the Encyclopedia of
Arda puts it at 5 years. Not sure where they get their info from, it sounds about right to me, although I have noticed several mistakes in their
First Age chronology before .
(I think they speculate sometimes when info is sketchy)
Morwen was in Dor Lomin looking for nobody most of the time.
Then, went to
Doriath.
She then went to
Nargothrond with Nienor for 'tidings' of the Blacksword (Turin) when Nienor & herself both disappeared in the
Glaurung debacle.
From that point on, no certain tidings of her fate ever came to Doriath.
All we know is she ended up dying at Turin's grave, saying "How did she find him?" to Hurin.
So, anything past that point is debatable.
It's really speculation - and highly unlikely at that IMHO - to say she was only looking for Turin & not Nienor from that point on.