I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
Texas does recognize a cause of action for private nuisance, which is what happens when someone engages in a course of conduct that interferes with the use and enjoyment of your land. Creating such noise that it is impossible to sleep for a several week period could be considered a private nuisance. However, you also have to show legal damage, which is something more than frustration. One way to do that is if they're causing any actual damage to your property. The other is to allege that you've suffered physical or emotional harm - that could require evidence that you've developed anxiety, a loss of peace of mind, and that the loss of sleep is causing you emotional injury (if it affects your ability to do your job, you can tell them that to).
It is possible to request an injunction when you file, asking a judge to order them to cease paying until they've put you up in a hotel. However, because you could go to a hotel on your own and then sue for reimbursement of the room (or you could buy a noise machine or noise cancelling headphones to dull the noise and sue for a refund), the judge may not order them to cease work. Usually, to get an injunction, you have to show that you're being harmed beyond repair - if they could repay you, then your harm can be repaired. Still, you can let them know that you're planning to file a lawsuit and give them one last chance to work with you. Talking to the construction supervisor isn't going to get you very far. He's probably not authorized to negotiate with you even if he wanted to, and his #1 priority is to get the job done. See if you can find someone to talk to in the company's legal department. They're much more likely to negotiate.
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