I'm a student in class 12. By looking at my performance in Physics, Chemistry and Mathematics, I think that I may not score high enough in my engineering entrance exams to get the subject of my choice, i.e. Computer Science.
Is it possible to make a career in computer science without a computer science degree? Is it possible to get hired like that?
Computer science is broad term that encompasses a lot. Typically if someone says they are in the CS field, they mean research. Which is going to be post-graduate degree work and then more.
If you mean software engineering, or networks, or just plain old programming, then you don't need a degree really. It'll be much harder to get a job (in the U.S. at least) but you don't absolutely need one. Many programmers that work professionally don't have a degree.
I strongly encourage looking for a CS program and getting a B.S.. Engineering, assuming you're into software, is somewhat wasteful. The degree is harder than necessary and much of the coursework will not directly apply to software. It might be a nice starting point if you wanted to branch off into another discipline later though.
More importantly, there are only so many credits in a 4 year degree...if you're taking less-applicable courses, more-applicable courses are being left out!
The bottom line is that you will need some kind of degree to get into the field. Perhaps a 2 year degree but you'll later go back and wish you did it right the first time. Trust me on this...
The degree just opens up the doors and in some companies allows you to advance further. It is just like with any other profession, you can't just come out of college and expect to be in the top level of the company, or even the middle level usually.
A degree is pretty much an expectation for any position these days. Many courses offer a year in industry - they'll help set you up with an internship for a year. If yours doesn't offer it, find one that does, because it's important; it'll put you miles above anyone who just has a degree. If it does, you'd better make damn sure you get it, even if you have to sleep with your professors while the janitor watches in the corner.