All _fundamental_ particles gets their mass from the Higgs (up to some issues with the neutrinos). Composite particles, say the Proton, is a strongly coupled system (that is, can not be described by perturbation theory) and it does not have the mass being the sum of its constituents (not even most of it). Hence, it is not known what gives most of the mass of particles such as the Proton.
Er, sorry, implicitly was talking about fundamental particles.
IIRC we do know where protons get their mass. The internal color field has some energy, thus some mass, which comes from that field interacting with Higgs.
