It sounds like the OP doesnt have the stamp in his/her passport yet but is expecting it very soon. I was in this position 4 years ago during the college app process. You cant say youre a PR before you have the stamp, even though you are expecting it. You would have to file all apps as an international student essentially, but making a note to each school that you expect a status change before interviewing or matricuating.
Unfortunately, if you'd rather not file as an international student, you would have to wait until you have a stamp/A number in hand. When I applied to med schools this past cycle, all secondaries asked me for the A number and every school I interviewed at either asked for a copy or to see the actual card on interview day to make a copy for their records. Even if you will have that stamp/ card in hand by the time you complete secondaries or interview, it will not be in your favor that the date you became a legal PR is later than when you first claimed to be on the primary application. (In fact, im fairly sure that is illegal)
I applied as an international student for college, btw and got my status change right in the middle of the process--did not end up affecting my app to schools or my financial aid apps, just file your AMCAS early and let the schools know youll be a PR soon.
I know how frustrating this type of thing might be, but hang in there, it will work out. PM me if you have other questions.