@Nicholas Moffett
You aren't going to get anywhere here with insightful, brilliant advice on how to win. I think the posters are unanimous in agreement you have no hope in winning such a case. I agree with them; however, here is a possible path to map out a strategy to win. Keep in mind this is probably advice to follow the lemmings and you will almost certainly waste your time and money pursuing it, but this is what you need to do.
First, and most important, consult a personal injury lawyer. For about $200 or less and 1 hour you can get a fast solid opinion in your jurisdiction. This is really a matter of case law, versus "the laws." It will all come down to how courts have interpreted the laws in the past. I am certain you are not the first to claim injury from second hand smoke or residue. Prior similar case outcomes are great predictors of your possible success.
You will need to show material (emphasize, bold and underline that word) impact to your health. "Material" does not refer to what could, might happen and it doesn't refer to what studies say happens. It has nothing to do with your opinion, no matter how well informed you are.
You have to prove the smoke residue actually DID materially affect your health in specific ways and that it could not be caused by anything else. You actually have to show that your cough is the direct result of breathing in that house. You can't just say it is, but rather medically prove it. It's not good enough to say you didn't cough before you moved in. This will likely be an expensive research project as it might require obtaining lung tissue contaminants and matching them to the residue in your home. That is why it is almost impossible to win such a case.
Suppose you got such a sample and made a match. You would show your lungs do have smoke residue that matches the house, but still might not be able to map it to be the direct and only cause of your cough. There also might be more there: smoke from campfires, pollen, asbestos, dust, etc. More medical research and doctors are needed to eliminate those as possible causes.
If successful so far, you have spent a lot of money. You will then need to show that your landlord actually provided an unsafe property. Your opinion is that it is unsafe; however, a judge or jury's agreement would be a massive leap in case law and effectively condemn half the properties in the jurisdiction, even if you have the medical evidence of the impact. Check case law - I am sure someone thought of this before.
I don't see any chance of success going after your landlord as mentioned; however, you mentioned another important fact. You wrote that you are required to work there to be with your clients. That makes it a workplace as well as a home. OSHA and other organizations govern workplaces. You may have an opportunity there with OSHA and workman's comp if you can show your workplace, not your living-space, but workplace is hazardous. Workplaces are regulated differently than living spaces and you might have a slightly better chance of success, but still probably very slim. Again, consult an attorney.
Good luck.
Jim.