Update!

The building manager, who is a very nice guy, just stopped by. I showed him all of the damage and he told me that a roofing company is supposed to come next week. (Apparently they're very busy, since every building in Los Angeles is poorly equipped for rain.) He promised to make repairs inside, and also (!) said that if we feel the need, we can move into an empty apartment across the building.

So I feel much better now. And also very full of tea, which I have been sucking down all day.