The contractor and possibly (depending on the exact circumstances) property manager are likely liable for any injuries, property damage, or costs you suffer due to their negligence, or unreasonable carelessness. You, however, an obligation to mitigate, or minimize, you damages and injuries. If your apartment is not habitable due to the dust, especially given your girlfriend's asthma, then you should get it professionally cleaned; save the invoices and invoices for any other costs (e.g. for a hotel until the space is cleaned) and then try to recover them from your landlord after the fact, including by filing a lawsuit (e.g. in small claims court) if necessary. Understand that since litigation is never certain, you may not recover part or all of your costs, but if you incur additional losses, damage or injury from your failure to take reasonable steps, you will almost certainly not recover for anything you could have prevented.