Organic wines are made consciously without use of chemicals and pesticides that are often found in crop farming and wine making. The main offender here is SO2 or sulphur dioxide, a preservative which is generally added in the winery. Those who intend to make wines without the use of these sulphite preservatives must be much more careful and ensure cleanliness throughout the winemaking process in order to make sure the wine does not spoil in the bottle.
In order to market a bottle as organic, you must apply for certification from an independently run body that checks your processes and finished product to ensure no synthetic chemicals have been used and that the site you are farming has been clean of chemicals for a certain number of years.
Is organic better? This is an open question and really comes down to personal preference. A wine made organically will often be of high quality as the fruit that goes into it will need to be clear of any imperfections such as rot that might cause the wine to spoil. The winemaking also needs to be thorough and carefully undertaken as without the preservatives, it can easily spoil and make bad drinking.
Is that why I’m red? For some people, the synthetic chemicals used can cause a reaction, if you have low tolerance to Sulphur Dioxide then you may find wine containing high levels might give you a red face or rash.