Just as a follow up to beaunydal's post... if you know I1 can never be "sick" (and is not part of the precedent range) then another non array alternative would be:

K1:
=CHOOSE(MATCH(COUNTIF($A1:$H1,"sick"),{0,1,8}),0,SUMPRODUCT(($A1:$H1="sick")*($B1:$I1<>"sick")),1)
confirmed with Enter
copied down