The SAT is only administered 6 times a year, and the registration date by phone for the May 2 test is March 31, so you’ll have to take the June test. I doubt that’ll be soon enough to be admitted for next fall. Here is the info. And as Suershbala said, the SAT is much easier than Indian exams.
You did hit a point though, if you’re already enrolled at an recognized Institute you might be able to apply as a Transfer student, in which case the SAT may not be required (though the TOEFL will). I suggest you contact a school and ask them about this, because I’m not entirely sure how US schools handle transfer admissions.
As well, as I mentioned before, schools in Canada and the UK don’t require the SAT. For the TOEFL, there are 3 test dates in May you can still register for in most major cities. One thing though- even if you miss the Fall admission deadlines, you can probably still make it into Winter admissions (Winter terms start in January typically), so it’ll only take a few more months and you won’t need to rush yourself.