Actually, I did apply with CIC and got rejected. However, the form says that if you have already submitted an application.
Sorry to hear that. IMO, they ask that to check if there is any CIC application submitted/pending which could be potentially converted when the nomination is received. But in your case the application was rejected ( i guess it was FSW) so there is nothing pending.
In theory there is nothing that can stop one from applying for AINP stream if FSW was rejected. Both have their own qualifying factors. So you should be good to go. But this is just my opinion. Let us see what other have to say about this situation. I am sure you are not the only one with this case.