What fiber crafts can I do when I am allergic to wool?
Yes, while you may lose some techniques that depend on wool's specific properties (like felting), there are a variety of fibers still available to the wool-allergic:

Other Animal Fibers Alpaca is the most common - but there are also other, more exotic ones - which may be tolerable.

Plant Fibers Cotton, linen, hemp. Should be completely tolerable even to the most wool allergic.

Synthetics Acrylic. Like plants, no crossover with wool, so should be safe. (This one may not apply to spinning, however, since synthetic yarns aren't made the same way as natural fiber ones.)

There's been at least one book written specifically for wool-allergic knitters ("No Sheep For You") and if you're on Ravelry, you can search the pattern database for patters written for non-wool fibers.