I don't think it is predominantly fossil (but see below).
More likely, it is concretionary. Concretions are often concentrically layered, the layers having slightly different chemisty. Sometimes conditions change, leading to some of the layers dissolving, leaving cavities. In some of those cavities, in this specimen, new minerals have been deposited; in one case granular clear crystals, in another milky botryoidal microcrystalline deposits.
Sometimes this sort of thing can form in caves (speleothemic deposits), and I cannot quite rule that out in this case.
Sometimes also, concretions form around a fossil as a nucelus. So I can't rule out there being a (small) fossil in your specimen.