Fleas 😒

So we moved into a new house, and the house is absolutely INFESTED with fleas. I'm due in early October, the baby could be here technically any time and I'm at my wits end for what to do. We have two cats and a small dog, should we just flea bomb the house? The problem with that is we have nowhere to stay while it's being fumigated. Are there any other options? I'm covered in bites and I don't want my baby to be covered when she gets here. Please any suggestions would be absolutely welcome!