Can you file an car accident claim if you don't have the other person's insurance information you only have his name his license's number address and his car's plate number?

Here is what happened,

I bumped into a car and nothing happened to my car neither to the other car. I tried to apologize, she kept yelling at me and said that has happened to her before and later she discovered an internal damage and she doesn't want that to happen again. I told her that I'll give her my number and she can contact me if she discovers any internal damage, but she didn't listen to me. All she wanted was my driving license, so, I gave it to her because I panicked and didn't know what to do. I also took her name, address and license's number then she left quickly without exchanging auto insurance information or phone numbers (she might have taken my car's plate number, I'm not sure. The car is not registered under my name, but my name is included in the insurance).

My question is, can she still file a claim to her insurance company without my insurance information? I'm afraid that she will give me troubles I don't need or accuse me with things that didn't happen. What should I do? Should I contact my insurance company and let them know? Should I try to get her number and call her or visit her, since I have her address, to see what is she planning to do? I'm afraid that this will show her that I'm afraid of her and make her do bad things to me while my real intention is to fix any damage I might have caused and avoid problems.