Yeah you have to be careful, but it's not like it's mission impossible or anything. There's a notebook (available for free) where all the illegal substances are listed. If you take meds or are going to chug something that is likely to enhance your performance, just check the damn list before you do it. It's really not that much trouble if the incentive is a chance to compete on an international level. Once you know that your Advil or whatever you guys eat in the States is legal you can take it all the time without even thinking about it. If you get a prescription, just mention to the doctor that you're an athlete and they'll prescribe a version of the medicine that is safe to use in competition.
Source: I compete internationally (not in skiing, though) and frequently take about 5 different kinds of meds and nutritional supplements (painkillers, allergy meds, antibiotics, vitamin pills and protein shakes).
PS. An Anvil Sinus is just an Anvil during the training season, even if you get caught. If you take it right before a comp it's more serious however, because it will actually enhance your performance. Be very careful with what you eat before important comps. Did you know that before precision disciplines, such as trap shooting, it's illegal to drink alcohol. It makes your muscles more relaxed, which improves your aim :)