Multiconfiguration Hartree-Fock (MCHF) and multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations are performed for the 2p(5) P-2 degrees, 2p(4)(P-3)3s P-4, 2p(4)(P-3)3s P-2, and 2p(4)(P-3)3 p S-4 degrees states of F-19 I to determine their hyperfine constants. Several computing strategies are considered to investigate electron correlation and relativistic effects. High-order correlation contributions are included in MCHF calculations based on single and double multireference expansions. The largest components of the single reference MCHF wave functions are selected to define the multireference (MR) sets. In this scheme, relativistic corrections are evaluated in the Breit-Pauli approximation. A similar strategy is used for the calculation of MCDHF relativistic wave functions and hyperfine parameters. While correlation and relativistic corrections are found to be rather small for the ground state, we highlight large relativistic effects on the hyperfine constant A(3/2) of 2p(4)(P-3)3 p(4)S(degrees) and, to a lesser extent, on A(1/2) of 2p(4)(P-3)3s P-4. As expected for such a light system, electron correlation effects dominate over relativity in the calculation of the hyperfine interaction of all other levels considered. We also revisit the hyperfine constants of 2p(3)((4)(S))3s S-5 degrees and 2p(3)(S-4)3 p P-5 in O-17 using similar strategies. The results are found to be in excellent agreement with experiment.