Unfortunately, nothing really has the weight or drape of wool except for wool. There are a few other animal hair fabrics out there that are similar in drape and warmth, but they're harder to find in a wide range and you'd have to make sure you're not allergic to them, too. Luckily, there are some really nice blends and synthetics. I'd start doing a crazy internet sweep for coat/jacket-weight and suiting tweeds. Order swatches of any potential candidate and compare to figure out which one you like best. If the fabric is all a natural fiber, you can order it white (or off-white or even a lighter blue in the same tone) and dye it. If it's got polyester in it, it has to be the right color (well, you can dye polyester, but it's harder).
I've found that linen at heavy weights has a similar drape as wool, but it doesn't have the same texture, so maybe a linen/poly blend?