Ok. She can apply for PR through the Buffalo office. And since you are her husband, she can (must) include you in the application.
The problem is what happens if you are deported while the application is being processed? CIC could ask for an interview, which you couldn't attend because you'd be unable to enter the U.S. again. Also, if you had your medicals done in the U.S. and were subsequently deported, you wouldn't be able to do a follow-up exam if they needed it.
You can solve these problems by going back to your home country. Your wife will still be able to sponsor you from the U.S., but you will have to spend some time apart. I suggest you do this anyway, because you're going to need to obtain a birth certificate, school records, etc. from your home country.
