We present thermoelectric power (TEP) studies under pressure and high magnetic field in the antiferromagnet CeRh2Si2 at low temperature. Under a magnetic field, large quantum oscillations are observed in the TEP, S(H), in the antiferromagnetic phase. They suddenly disappear when entering in the polarized paramagnetic state at H-c, pointing out an important reconstruction of the Fermi surface. Under pressure, S/T increases strongly at low temperature near the critical pressure P-c, where the antiferromagnetic (AF) order is suppressed, implying the interplay of a Fermi surface change and low-energy excitations driven by spin and valence fluctuations. The difference between the TEP signal in the polarized paramagnetic state above H-c at ambient pressure and in the pressure-induced paramagnetic state above P-c can be explained by different Fermi surfaces. Band-structure calculations at P = 0 stress that in the AF phase the 4f contribution at the Fermi level (E-F) is weak, while it is the main contribution in the paramagnetic domain. In the polarized paramagnetic phase the 4f contribution at E-F drops. Large quantum oscillations are observed in the antiferromagnetic state while these disappear in the polarized state above H-c. Comparison is made to the CeRu2Si2 series highly studied for its (H,T) phase diagram.