We analyze the charge and spin distributions induced in an interacting electron system confined inside a semiconductor quantum wire with spin orbit interaction in the presence of an external magnetic field. The wire, assumed to be infinitely long, is obtained through lateral confinement in three different materials: GaAs, InAs, and InSb. The spin-orbit coupling, linear in the electron momentum is of both Rashba and Dresselhaus type. Within the Hartree-Fock approximation the many-body Hamiltonian is diagonalized directly and its eigenfunctions and single-particle spectra are obtained selfconsistently. Further, we calculate charge, and spin densities, as well as the charge and spin currents and compare them with those obtained in the absence of the interaction. Thus we observe an enhancement of the spin polarization associated with the spin-orbit intreractions, on account of the exchange Coulomb effects, in GaAs, but not in InAs and InSb. However, in the later materials the direct Coulomb interaction may amplify or modify the spin currents.