The people couldn't move me to the hospital and the doctor operated on me at home.

Given sentence is in active voice(compounded using 'and ') and change it into passive voice. 

Since there are two simple sentence and we should change the voices of both the sentences 

It is in the form of ' sub1 + modal auxiliary +not+ V1+ obj' and ' sub2 + V2 + obj'

It is to be converted into the from of ' obj+ modal auxiliary +not+be+ V3+ sub1 and obj + was/were+ v3 + by+ sub2'.

In this case we can eliminate the group of people. Simply I couldn't be moved conveys the actual meaning. Then the word ' I ' don't need to place again. since it's connected using 'and'. 

So the correct answer is A.