Can I say I'm facing a unique temptation that no one has ever faced?
No. Scripture teaches that no temptation has taken you except what is common to man, so you cannot claim your situation is unique. Christ Himself has already passed through every category of temptation, though He did not fall, making Him able to sympathize with your infirmities.
In Hebrews, the point is that we have a high priest who can be touched with the feeling of our infirmities, because He was tempted in all points as we are, yet without falling. Then in I Corinthians 10:13, Paul writes that no temptation has taken you but such as is common to man. So Les explains you cannot say you are in a unique position or that no one has ever faced something like this before, because Christ Himself has. The contrast is that we fall, but He did not.
There hath no temptation taken you but such as is common to man: but God is faithful, who will not suffer you to be tempted above that ye are able; but will with the temptation also make a way to escape, that ye may be able to bear it.