We investigate the effects of screening on polaronic corrections to the effective band edge in photoexcited quasi-one-dimensional GaAs quantum wires and two-dimensional quantum wells. We develop a variational method to calculate the polaron energy of a two-component plasma (electrons and holes) coupled to LO-phonons. Screening effects are incorporated within a dynamical scheme. We find that the screening effects and finite well width considerably reduce the polaron energy as the plasma density increases. Many-body corrections beyond the random-phase approximation are also considered.