I can understand your situation, but the first thing i will tell you is, if you really want to study PCM, you must have your reasons right?

Look into those reasons first, are you sure they are justified? Maybe you want to be an Engineer someday,but is that really what you want? Look into it.

Then, if you still believe, you really want to study PCM, then, don't fret about the reputation of schools. Because nobdy will ever ask you where you did your 12th std from. College, it matters. But schools never do. So choose any school that is offering you the Science stream without hesitation, and focus on studies and then getting into a good college. 

You need to apply to all colleges online for class 11th admissions. Based on your class 10th score you shallbe allotted seats as per cutoffs for your preferred colleges .
You can fill up maximum of 10 college as per your preference and accordingly you shall be called for counselling.

You can fill up the form on this following website:

http://mumbai.11thadmission.net

All the best.