You were informed that the premises contained asbestos. When drilling occurred in the walls, you did not object. Guess what ?

You’re basically on your own. You rented the premises, knowing full well that same contained asbestos, and agreed to rent anyway. You were also advised that drilling in the walls could increase your exposure. You also allowed the drilling.

Environmental Health, it is a county office.

They will test for free if they really think there is a threat, but unless you were the one doing the drilling and you were inhaling without a face mask I doubt there is much risk. They will still test for you though, you will just need to pay for it, not the tax payers.