Do the transparent, viscous secretions that appeared after Tawaf count as madhiy, thus necessitating a repeat of the Tawaf, knowing that the questioner suffers from obsessive-compulsive disorder and adheres to the opinion that ablution is sunnah for touching women?

All that you feel regarding something exiting from you is a whisper (waswas), so ignore it. As long as you are performing ablution according to the Sunnah for the circumambulation (Tawaf), there is no harm upon you, and this is a strong opinion. Perform ablution for the Tawaf, and then do not pay attention to any doubts that may arise thereafter. Your 'Umrah is valid, Allah willing.