"Natural" doesn't mean hypoallergenic, safer for skin, or less likely to cause irritation. In fact, the term "natural" isn't regulated by the FDA at all--something could be called "natural" that came right from a test tube. (For that matter, there's no legal definition of the term "hypoallergenic," either, and companies can use it anywhere they like.)
If you have allergy issues, it's a good idea to find out which thing's causing it; chances are it's a natural ingredient like lanolin or essential oils rather than inorganic materials like silicone derivatives. That's not to say synthetics won't disagree with your skin, but irritation isn't the same as an allergic reaction; inert inorganic stuff is highly unlikely to cause allergies.
The term "organic" IS regulated, but organic cosmetics also spoil more easily and can become repositories for pimple-causing bacteria, so they need to be stored more carefully and replaced more often. Also, if you have a known allergy to strawberries or lemons, you may find that organic cosmetics containing them trigger the same release of histamines that eating them would. (I found this out the hard way when an all-natural lip balm gave me Lisa Rinna lips for two days. Yikes!)
Forgive me for kinda going off on a tangent. It's just something I know a bit about because I'd written some articles on the subject and was downright shocked to find some of this stuff out as I was doing my research. I thought it might be of interest to y'all, too.
