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Answer: You have two separate issues here. As far as asbestos exposure, you may want to contact a local area law firm that handles only asbestos cases. With only two days exposure and no medical bills, it may be a hard case to win or settle now; but the can put you in touch with a medical expert that they usually have on staff or routinely deal with and get you most likely a free diagnosis and an assessment of your claim.
As far as gaining access to your land, you may want to enter into a temporary construction access agreement with them in exchange for compensation. This is also known as a license and protection agreement in NY.