Mold and home not in living conditions

Rented this unit and the unit had a musty smell. I assumed it was because is old but it was not. After a week of living here, I noticed my kids and I kept getting sick. I kept mentioning this to landlord until they sent a cleaner. Cleaner found lots of cat hair as well as mold. I also had to change the air filter myself which was completely full of dust. Inside the air filter compartment there was a lot of dust also and black stains. After these findings, I reported to landlord's right away and they did not do anything to remedy the situation. At this point this is an urgent matter and we keep getting g sicker and sicker. This is prime example of cutting corners. I tried to open windows to let some fresh air in and was only able to open one window. The others are stuck shut which is a huge safety hazard.