It sounds more like a psychological problem to me, it isn't really possible to be allergic to books in general as they may be made from differing types of paper and different inks used to print them. The allergy would then show up when handling leaflets and newspapers as well.
If the books that cause this itching were all very old and from the same source then it is (barely) feasible you have an allergy (sensitivity) to the dust contained within the old books but that would be more likely to present as breathing difficulty.



