Cool, well a University degree is a University degree, it doesn't have to be aviation related to get a job in aviation. It is essentially a requirement to get into the majors these days in the US (amongst other requirements).
If you have a green card, you will be treated about the same as anybody else unless the job specifically requires eligibility to get a security clearance.
On a final note from me, if you already have a job instructing, keep it unless you think the business is about to go bust. If you are currently jobless, then going to the US might be a good move for now, but have no illusions of making bank (see check airman's good post above)