From the Scriptures
Quran narrates for us the story of Prohpet Abaraham (puh) who despite being a prophet wanted to set his inquisitive intellect at peace.
Call to mind the other event also, when Abraham said, "My Lord, show
me how Thou bringest the dead back to life?" He said "Have you no
faith in this?" Abraham humbly replied, "I do believe but I ask this
to reassure my heart." ... (2:260)
Another example is quoted of, who is believed to be Prophet Ezra (puh):
Or take the case of the one who passed by a township that had fallen
down upon its roofs. He exclaimed, "How shall Allah bring back to life
this township that has become dead?" At this Allah caused him to die
and he lay dead for a hundred years ... (2:259)
We may not say that prophets had doubt - in the general sense of the word "doubt", but rather the quest to attain greater surety of faith as corroborated by Quran:
And thus We showed Abraham the kingdom of the heavens and the earth,
so that he might become one of those who have sure faith.. (6:75)
The point to be taken from these verses is that faith does not come as white or black, but rather as a grayscale of certainty.
There is probably no greater exponent of doubt as the first step to certainty than Al-Ghazali, one of the most influential figures of medieval Islam. In his autobiographical work al-Munqidh min al-Dalal (Deliverance from Error), he narrates how be became a skeptic until he could no longer rely upon neither his senses nor reason for curing his "disease" of doubt and attaining "certain knowledge." There is a school of thought, including orientalists, who trace origins of Descartes' doubt to be in Ghazali's Munqidh.
Let me quote directly from Munqidh. I strongly urge you to read the whole treatise.
Certain knowledge is that in which the thing known reveals itself
without leaving any room for doubt or any possibility of error or
illusion, nor can the heart allow such a possibility. One must be
protected from error, and should be so bound to certainty that any
attempt, for example, to transform a stone into gold or a stick into a
serpent would not raise doubts or engender contrary probabilities. I
know very well that ten is more than three. If anyone tries to
dissuade me by saying, No, three is more than ten, and wants to prove
it by changing in front of me this stick into a serpent, even if I saw
him changing it, still this fact would engender no doubt about my
knowledge. Certainly, I would be astonished at such a power, but I
would not doubt my knowledge.
Thus I came to know that whatever is known without this kind of
certainty is doubtful knowledge, not reliable and safe, that all
knowledge subject to error is not sure and certain.
Have I answered your question directly? I'm not sure that I have, but I have endeavored to show that your condition in not unprecedented in the history of faithful.