I don't know that any US carriers will go out of they're way to sponsor you, but they def won't discriminate as long as you have the right to work here.
With that experience you should be pretty competitive, but equally as important as flight hours here, are who you know. All the "shortage" drama you hear about is for the $20,000yr regional FO jobs. All the mainline carriers are swimming in apps. Internal recommendations go along way, and for that reason you'll hear about guys with your experience and more who can't get a call. Then you'll hear about a 2500 hr RJ FO that lands his dream gig at Delta.
That said, throw your app in and go for it!
Also be aware, they may not fly you all the way from the ME to the U.S. to interview. What's a degree equivalent? US carriers require a degree from an "accredited" University, I'm not sure If many schools outside the U.S. and Europe are qualified.
Either way, Good Luck!