Both previous answers are great already, i just want to add some more insights.
As Samuel said s'inquiéter works as a whole.
s'inquiéter
je m'inquiète se --> me
tu t'inquiètes se --> te
nous nous inquiétons se --> nous
etc...
To add to what Benoît said, here are 2 sample sentences :
- ne reste pas au milieu de la route, tu inquiètes les automobilistes.
(do not stay in the middle of the road, you are worrying the drivers)
- comme tu ne donnais pas de nouvelles, je me suis inquiétée pour toi.
(since you gave me no news, I was worrying about you)
Now about your question : I worried myself stupid.
I'm not sure exactly about the meaning, here are some suggestions.
- Je me suis inquiété comme un con (I worried myself unnecessarily)
- Je me suis inquiété comme pas possible (I worried myself like hell)
- J'étais terriblement inquiet (I was terribly worried)
- Je me suis pris le chou (I was getting mad thinking about it)