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It's quite possible that just the extra dust in the air is what's causing your discomfort. If the job is permitted then I doubt there is any long term health hazard like lead or asbestos. But just a lot of dust in the air can cause respiratory problems
Since the contractor is EPA certified it's not at all likely that he is disturbing lead paint or asbestos.
If there is dust covering the hallways then you can be reasonably certain that there is significantly more dust in the air than normal. This can lead to short term problems like you describe. You can call your local board of health and ask for their input.
In general with house-bolting are there generally abatement or containment procedures that are implemented? Or is it work that does not require such steps? I don't really understand what it is they're doing, so it's hard for me to wrap my head around.
They could be drilling into the foundation concrete/stone or even minor demolition in a house of this age will put a lot of dust into the air. So will cutting wood. Most remodeling project stir up a lot of dust which is usually not harmful on a long term basis but can be irritating and cause respiratory problems on a short term basis. I can't give you medical advice as to how long you would have to be exposed to nuisance dust for longer term respiratory problems to occur.
Okay. Yeah, I know you can't give medical advice, but I figured home improvement experts would have a better idea than I about what they're actually doing and how likely it is to involve disturbing lead/asbestos. Which is all I'm really worried about. Thank you!