With hayfever the symptoms for each person depend on the particular plants which flower in an exact time period.  So the reappearance of symptoms would be both longer and more random.

Heart disease which can cause the symptoms is likewise likely to be both more continuous - and not contagious at all.

Viral illnesses can manifest in re-occuring waves, though these cycles usually appear to be of shorter duration than you describe, being timed with the infection/internal replication/destruction and release phases of viral cell-colonists, giving a pattern repeating within a few hours - like malaria (although that is another type of cell parasite).  This cycle is not the only viral one however.  Occasionally the virus, beaten back by the host's immune system, retreats and hides within difficult to reach tissues.  This can then return when the monoclonal antibodies (and the cytokines which instruct your system to manufacture them) that controlled it drop back to more normal levels.  When these illnesses return they often appear more severe, as the body recognises its failure to eradicate them the first time and makes more cytokines this time.  It is these which produce most of the symptoms (we call the symptoms viral but it is actually our bodies response to them which produces the symptoms - the same response which causes hayfever symptoms as your body thinks itself under attack from pollen too).  They are quite contagious as well!

This all suggests a viral illness to me.