Can I be sued for $3,000 for a car accident if ...

Yes, anybody can sue for almost anything. Getting paid is another story. Claims under $5,000 go to smalls claims court to help avoid the courts be over loaded. There, a judge will say who gets paid or not. (Then comes the problem of collecting the judgement.) Sounds like you have no choice but to go to smalls claims court and give your side of the story. If you don't go, that's another problem I don't think you want. The judge will just rule against you.

First, let me see if I understand what your saying. You were in an accident that was your fault. The party you had the accident had his car fixed by his insurance insurance company. Now you want to know if he had his car fixed by his company why he is sueing you. If that is what happen, most likely it is his insurance company that is sueing you to recover their loss. They have his subergation rights to go after you.