Check the noise ordinances in the area, but remember to check the zoning too--residential zoning has different requirements than business zoning. My street is zoned as residential so they aren't allowed to start road work or construction before 7 a.m. but we're a block and a half from a main road that is zoned for business and in THAT area they are allowed/required/encouraged (not sure which it is) to do road work and construction overnight, so as not to impede business traffic during the day, so when they are working on sewer lines and potholes and such, we put up with klieg lights and jackhammers all night. Depending on the zoning of your building, they may well be within their rights to start construction that early.

If you can't find a law to back you up, you can go to the housing office and see if you can get out of your lease on medical grounds--if you're having migraines triggered by the current situation and they can't stop the situation, they can at least let you out of your lease so you can find a quieter place to live.

Good luck!