Yes, if there were claims made due to you being at-fault in the accidents then the auto insurance company would have records of this in the form of your claims history.

Even if you change insurance companies your claims history can be looked up any insurance company by using the Comprehensive Loss Underwriting Exchange (CLUE) database. Through the CLUE personal auto claims report an insurance company can receive a person's 5 year history of auto insurance losses.

How the CLUE database works is that insurance companies feed information about property loss claims, even inquiries about coverage, into a central database. So claims filed against your auto insurance policy for losses you caused in your two accidents would be placed into this national database

The CLUE report thus could show any new insurer information about any claims you filed under your previous insurer's policy. CLUE also includes information about inquiries you make, even if a claim was never submitted or paid.

Your CLUE report will include date of the loss, the type of loss claimed and amount paid by the insurance company for the loss.

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