I will add on to the comments from those who've strongly recommended that you contact your insurance carrier. In cases like this, since you have been put on notice by the client of their alleged injuries, you need to notify your carrier as soon as possible, because you DON'T want there to potentially be a ROR (Reservation of Rights) due to late notice of the claim.
Every insurance policy is different; however, most insurance policies have language within their policies as to what an insured needs to do when a loss occurs, and to report the claim in a "timely" fashion. Obviously there is some subjectivity in regards to timely, but if you know about an alleged loss a day or so after it occurs, but you don't notify your insurance carrier for 3-6-9-10+ months, the longer it goes, the worse it potentially could be for you as the insured, of the insurance company denying you representation for the loss due to late notice. And given that you've posted this on a public site, it would be difficult for you to later explain why you didn't report it to them sooner when you posted it immediately on a public site...just food for thought.
In general, my personal recommendation would be that ANYTIME someone is alleging any type of personal injuries, that you report it to the carrier ASAP. If it's a property damage claim for a minimal amount (again, minimal being subjective, but I'd say for most people and NOT businesses, maybe under $1,000), then I could see you potentially wanting to pay it out-of-pocket and letting the person go on their merry way. Again, that is JUST a personal opinion, and definitely one you need to think about before paying anything out-of-pocket, because you don't want to put yourself in a bad predicament with the insurance carrier, since you have now muddied the waters and paid some monies when they may, in fact, have denied the claim it's totality, and by you making any payments, you've possibly put that denial at risk.
I'm over simplifying the claims process, but I just want you to be aware that alleged injury claims, in my opinion, should be reported to the insurance carrier to handle.