Uninsured motorist, not at fault. What are my rights?

I was involved in an accident recently. She cut me off and slammed on her brakes. To avoid hitting her passenger side, I swerved and clipped her bumper. I was uninsured at the time due to having to cancel my insurance because I wasn't even making enough to pay my rent let alone car insurance. I now have insurance, but she's coming after me for $3,000 when her bumper had a fist sized dent. The paint wasn't even chipped! I was wondering what are my rights, because it doesn't seem far that I have to pay for her poor driving.