Can a person submit an auto insurance claim after she was paid for half of the damages and then she decides to make a claim?

Paid by whom? And for what were they paid? It sounds like she took on the claim herself. In this case it will be very difficult to later want the insurance company to take over the claim and expect to receive payment from them as well. The insurance company in not going to want to take over a partial claim and they may not be able to legally do this depending on the state laws where the accident occured and where the claimants reside.