You can use all these sentences to say you had become sick: all of them are refering to (me) "enfermé de forma repentina" "me puse enferma tras un día muy agitado" "estuve enferma durante cuatro días" "padecí una enfermedad contagiosa" "tuve una enfermedad que me provocó debilidad"

Me había enfermado.

me he enfermado.

Me había enfermado. I had become sick. Me he enfermado. I have become sick. You wouldn't really use the phrase "I had become sick" without some other point of reference in the past, and equally so in Spanish. When it was time to go I had become sick.

Me he enfermado.