Getting a loan doesn't seem impossible once we have our EAD and SSN. Still, things are much more easier to do with a green card. I'm also from NY. Plus, doing residency seems possible if you can work. The problem is hospitals might be considered as government department/ jobs, which will require green card to apply.
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Application date: 5/12/16
biometric: 6/20/16
Approval: 10/13/2016
Expiration: 9/4/2016