If I have doubts about my faith, as Thomas did (and I do, pretty much every day), am I questioning my belief in God?
Yep. But I don't see that as a bad thing, because my beliefs about God are not, after all, God.
Questioning my beliefs about God can help me discover the newness of God every day, and in discovering that newness, I grow with God instead of toward God. The difference in those two words is everything: toward implies a distance between me and the Divine, whereas with implies an intimacy.
Doubt did not prevent Thomas from an intimate encounter with the Risen Christ. On the contrary, it became a blessing: doubt led Thomas to declare "My Lord and my God!" (John 20:28)
Doubt is not a barrier to true faith, certainty is. Doubt invites us to seek out the more of God. Doubt inspires us to see God more clearly, love God more dearly, and follow God more nearly (to paraphrase St. Richard of Chichester) Certainty, on the other hand, traps us in petrified ideas. We my find comfort and security in certainty, but certain belief is dead belief, because there is no need to learn anything more, no need for growth. But God is the God of the living, not the dead (Mark 12:27), and life always grows, changes, and adapts.
I do not need to fear doubt; rather, when faced with doubt, I need to ask, "Lord, where are you inviting me to go?" Far from being an impediment to spiritual growth, doubt is an invitation to deeper conversion.