As someone coming from India, I think I somewhat understand your concern. Here are some stuff I would suggest. First, you need to figure out if you really LOVE programming. By "really love" I don't mean just working on homework assignments, but are you that kind of a person who would create apps or code something just out of fun? If that is indeed the case, or you know for certain that you can really do well in coding, then getting a job in a software development field should not be any problem for you. And I can assure you that a person who loves coding is a great asset in a company, irrespective of what she majored in.
Also, you will most likely have "on campus" interviews in your final year of college. At least when we were in India, students from all fields (mechanical, architecture, civil, etc etc) got picked up by companies like TCS, Infosys, etc. In that case you will get your most needed break in the software world and then take it up from there. These companies also train you initially for a few months. Don't worry about the big name companies at the start of your career. Your main goal now should be to learn and gain experience.
In the mean time, do focus on a specific language that you like (C# or Java, maybe) and strengthen your Data Structures foundation. Also, like Ms Manzo pointed out, you can always go for an MS (or MTech) in Computer Science and Engineering. Don't hesitate to ask me more questions :) Good luck!