No, the Saint Pau's schools one was thinking of are in NYC and were formerly Saint Vincent's. This is why you need to give detailed information when making posts! *LOL*
Anyway there is no use sweating things until you know what the decision is regarding your appeal. Until then concentrate on doing well (as in an "A") in your remaining classes.
Yes, there is a very good chance that other nursing programs will not accept you for admission, but we've covered that already. Even if they did you'd probably have to apply as a new student and repeat at least the nursing classes.
If the worse comes to it, you have a few options though neither is certain.
Finish your associates in another major, then go on for a four year degree. Afterwards apply to a second degree RN program. Be warned many BSN programs again will not accept a student that was removed from a previous nursing school for cause. However there is the chance you may be able to find one that will overlook your past on that matter.
Finish your associates in another major then try for a LPN. If you succeed there once licensed go for a bridge program to become a RN.
Either consider transferring or applying as a new freshmen to an ADN program elsewhere in the state that will take you. See above, but again you never know.
Finally there is the Excelsior program: Excelsior College | The School of Nursing at Excelsior College
Before leaving will give my standard advice to persons in your situation. Before rushing out to get back on the nursing program horse, some sort of deep soul searching should take place. All nursing programs are not easy, and if you failed out the first time what if anything will you do if or when you are admitted to another? Look at your grades and take an honest evaluation of your efforts. If you really gave the best you could and still couldn't pass the first time, what makes you so sure you'll do so the second time around?
The fact you failed *two* nursing classes is troubling. If you were sitting on the fence with barely a "C" average or whatever minimum for passing was at your former school, that is sitting very close to the window's edge in any nursing school. It means one push and out you go.