I was told that my circuit will not work.
what is wrong?
what can I do to fix it?
can I use a different IC?

 

Who told you the circuit is wrong? It looks to be just following the typical appliction example in the datasheet. Did they say why it wouldn't work? Admittedly, driving 10 LEDs with a typical Vfwd of 1.8V is pushing the limits.

 

I was told that my circuit will not work.
what is wrong?

Why not ask that person, since I would assume he has a reason for that statement?

 

I don't see the problem.
I would use the B version. Less power lost in R26 and you save 1 volt on the "too close to 20V" thing.
You might change C18 so it connects to ground, or just remove it.