LZ mentioned "因为我的保险是最基本的那种(也就是有些朋友把它叫做“单向险”的那种)", that's liability insurance.
I myself only purchased the liability insurance just as LZ did. Per definition, Liability coverage pays for your legal responsibility to others for bodily injury or property damage. My insurance will pay for others, not for me.
I had two, three occasions of accidents for the past 10 years. Luckily i wasn't at fault for all of them. each time, i dealt with the other driver's insurance company for car repair/rental.
in lz's case, the other driver has accepted the responsibility. the best way for lz to do is to file a claim against the other driver and let them pick the cost for everything.