My experience in aircraft is from the maintenance side, not the engineering, but I was heavily interested in aeronautical engineering at one time before my academic pursuits took me elsewhere, and I eventually served as a career adviser at a major university in Texas, USA for a time.
When we speak the term "aerospace" it means what "aeronautical" used to convey, except that today low Earth orbit is now considered a partial component. Most of the basic education, until you specialize, would focus on aerodynamics, mechanical engineering, mathematical analysis, with lab components including basic design, wind tunnel testing, stress loading, etc.
It is in a way a "capstone" engineering science, bringing together multiple disciplines into one.
If your math is outstanding, you will have no trouble. If your math is merely good, brush up now. My math skills were what kept me from pursuing this endeavor.
In the US, there are major employers for aerospace (Boeing, Lockheed, Raytheon etc,) and there are many subcontractors that both supply them directly and provide contract maintenance for civilian airlines and the military. Different venture capitalists have launched their own private space ventures; close to my home, SpaceX has a rocket engine testing facility, and a division of Raytheon provides avionics refits and aerodynamics modifications.
Boeing and Airbus are really competitive. They both are major project contractors, meaning they will take on huge aerospace projects and manage them, not just build airliners. I wonder if either of them would have a program to help an international student get an education either in their country of origin or the country where incorporated/manufactured/managed? They may even have been involved in some of India's recent space efforts, even if just lending a hand out of good will. It's not outside the realm of possibility. I'd look into it.
Once you have all of the qualifications, a US work visa shouldn't be a problem, but I am not a member of US Immigration and am no authority on the matter.
EDIT: Go
here and read the thread on questions a US student has on becoming an AS engineer. They're a bit more basic, but there are two engineers with posts in it,
Dr. Courtney, who has taught at the Air Force Academy, and
boneh3ad, a Science Advisor, who is an aerospace engineer.