Hi Mora -
I think your adorable young law student has a lot to do with this dream! Are you worried about getting pregnant right now?
Cars in dreams typically represent ourselves. As you wrote, “It has all my stuff in it.” You were driving along, when suddenly an unexpected baby appeared before you. You dropped everything to take care of the child - and in the process lost your car. I think this part of the dream reflects your concern about an unplanned pregnancy right now - and what effect it would have on your life. As you understood in your dream, you would have to “drop everything” including many of those plans you have that are represented by the car - which is your direction, where you are going!
I find it interesting that you give the child away to a large family. I believe this reflects your sense that you are not ready yet for a child. It might also reflect the thought that, if you did become pregnant, you might give the child up for adoption to a “large family;” humanity.
My recommendation? Safe sex! Share your dream with your lover, and insist on using birth control. You’ll enjoy each other even more then.