You would be very hard-pressed to find a respectable historian who believes that Jesus did not exist. There is arguably more good evidence that Jesus existed than did Alexander the Great. Whether or not he did all the things he is reported to have done is perhaps another matter. The issue of Jesus’ existence, however, is so well established historically, that it is almost never seriously disputed.
A burdened heart doesn't equate to a lack of faith. The God of Abraham, Isaac and Jacob can heal with a simple command. The burden comes from wondering if that's His will and may it be done.