I got into my first car accident?

so i've had my license for a little over 2 months. and i was driving today and luckily no one was hurt but my whole passenger side is screwed. i was driving down the road and the car just pulled out of there parking spot and boom. the police said it wasnt my fault, i didn't get a ticket, and the person who hit me insurance has to pay for everything. but will they? thats what i'm most nervous about. how does this whole thing work? will this make my insurance go up? even though it clearly wasnt my fault, as my car is completely damaged and hers was not nearly as damaged.