Children and the elderly, especially those who're very sensitive to chemicals are more prone to VOC related illnesses. What's alarming is that the indoor air is more polluted than what you breathe outside your house. The Environmental Protection Agency is hence trying to get a VOC regulatory policy that would enact laws to limit the VOC content. You could also help reduce the VOC levels by increasing the concentration of fresh air in the room; have more ventilation outlets. Try and maintain the temperature and humidity at optimum levels as chemicals produce VOCs when it's more humid and the temperature is high. Look for VOC sources and do away with them. Stored chemicals should be discarded as they could leak and lead to a possible VOC health concern.
Paint manufacturers are developing zero VOC paints and low VOC paints. Zero VOC paints have 0 grams per liter (Benjamin Moore Natura). Low VOC paints should not contain more than 50 grams per liter (Benjamin Moore Aura). You must note that environmental laws specify different VOC levels for different products; varnishes have a different limit than paints, metal paints have different levels than wood paints. If you're allergic to the typical paint smell, environmentally friendly paint is a boon for you as it's also virtually odorless. These paints are easy to dispose off as they are not considered to be a hazardous waste. Generally, renovations including repainting should be done when the house is unoccupied. You may also have to wait until the odor wanes. But with zero VOC paints, you could move into the house sooner. If you're using a low VOC paint and are slightly allergic, use a paint whose VOC level is not more than 50 grams per liter.
Remember to read the product label carefully before buying or using any product. Follow the instructions given. Look for what EPA has to say about the paint. Whatever the paint, buy only the amount you need. Switching to such a zero VOC paints maybe a small step for you, but would have a huge positive impact on the environment.