@Ruslan47
Just to clarify, what is this construction? Is it something the host is having done in the building or someone else? If it's someone else, I agree with @Sarah977 that there's nothing she can do about it now and that you should contact Airbnb and ask to be relocated and refunded the rest of the stay. You can't stay and then expect to be refunded, if that's what you were hoping for.
I do agree with you though that's it's dishonest for the host to claim that the information was there when you booked, if it was not, and she should at least have warned you about it as soon as she knew.
I have a noisy construction site near me. It's not too bad now but was very loud at first with the floors vibrating at times. The local council didn't bother notifying me of it, which they should have done, so the guests staying at the time were not prepared. Luckily, they were very understanding (they could see I was totally surprised about it) and neither complained nor rated me down for it.
I of course notified any upcoming guests. I haven't mentioned it in the description as the building was supposed to have been completed by October, but I do inform all new guests about it before they book just in case it is not finished before they come. No one seems bothered by it so far, but at least I gave them the heads up!