(Sorry for the thread-jack!) Theodora, you aren't nuts. You probably have sensitive skin, but not a wool allergy. When someone says that they have a wool allergy, I take it to mean that a person likely has a sensitivity to the itchy stuff not a full allergy unless they say that it makes them non-stop sneeze and break out in hives. A wool sensitivity is just as legitimate a reason for not wearing it! Who wants to be uncomfortable!?!
Your older wool sweaters probably have a few things going on. They likely have had all of the natural lanolin taken out by repeated cleaning. Lanolin can be irritating to some people. They also likely were made with wool that was virgin, meaning it has the natural, tapered tip from when it grew out of the skin, not a cut tip from a previous shearing (think of it like the difference between a new hair growing out and a hair after your haircut). The blunt edge is generally more irritating. Also, the longer the length (staple) of the wool, the softer it is because they can make more yarn out of it with fewer ends, resulting in softer yarn. Think of the number of ends in a tangle of full length spaghetti versus the number of ends if you take the same spaghetti and break it into 1" sections. You still have the same amount of spaghetti, you just have a lot more ends. It may also just be better quality wool from sheep with softer wool or from longer wool with fewer ends, even if it isn't virgin wool.
With the shearling coat, that's probably exactly what is going on. Shearling is generally made with hides from sheep breeds with very soft wool and the wool is relatively long because the animal is raised for that purpose and not for repeated shearings. Cashmere and angora are both super soft and come from goats, but are still hair like sheep's wool. Alpaca is also generally super soft and can be worn by many people with wool sensitivities. However, any of them (cashmere, angora, alpaca) can be itchy when they are lower quality (which can even just be the same animal, but a different location: belly versus back) or combined with lower quality wool or (yikes!) expensive but bristly mohair. The nice thing about this? You can trust yourself on which wool will work. You just need to let your skin be your guide!