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I am sorry to hear this.
Who is trying to put the blame on you? Jiffy Lube or their insurance company?
So what you can do is send a letter to Jiffy Lube by Registered Mail. Give them a deadline to pay you. Tell them if they fail to comply you will commence legal proceedings and then be seeking interest and your costs.
Then if they don't comply you should start a claim in Small Claims Court. You can self-represent and if it gets that far and you find you need some help as you go through the process you can always post on this site again and I can assist you further.
Does that help as a starting point?
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Is there anything more I can help you with at this point in time?