Is my undergoing a necessary surgical procedure that requires the uncovering of the severe nakedness (awrah mughallazah) by a male doctor considered a worldly دفع for my religion, and is this a weakness in faith and abandonment of reliance on Allah?

The basic principle is that it is impermissible for a woman to be treated by foreign male doctors if there are female doctors available, whether Muslim or non-Muslim. However, if the rupture of the hymen leads to an inability to marry, or to accusations against one's honor, then this is a recognized need that is akin to necessities that permit the forbidden. In such a case, treatment by the aforementioned man is permissible. What you did is not an indication of weak faith or contrary to reliance on God, because seeking treatment is commanded by Islamic law.