Yes, we all question God in the face of inexplicable suffering, even though the bible shows that good people suffered terribly (like Jesus and the disciples).

My advice would be accept the doubts instead of fighting them. Maybe God will work through your doubt as you struggle with faith.

But also, put into your life a preponderance of those things that are faith-building rather than faith-shattering. Scripture, apologetics writings, association with people of faith, articles by people who have drawn close to God through suffering are all ways to nourish our faith when an unbelieving world would lead us in a different direction.