Different paint products use different ingredients, so it is difficult to comment on the health effects of paint in general. However, health effects associated with the paint will be significantly diminished as the paint dries. The best thing that you can do is to create conditions inside your home which would encourage a more rapid drying of the paint. The chemical process that occurs during the drying of paint is called evaporation.
Evaporation is where the liquid portion of the product changes from being a liquid to being a gas.
Just because it vaporizes doesn't mean it disappears altogether. For example, water liquid and water vapor are both still water, they just have slightly different properties. During the process of evaporation, another process occurs - dispersion. The best illustration of dispersion is when you take a bottle of cologne and open it in one corner of the room. Within a few seconds, you can smell that cologne clear across the room, even if the bottle has not been moved.