We present the detection of excited fine-structure energy levels of singly ionized silicon and neutral carbon associated with the proximate damped Lyman-alpha system at z(abs) = 2.811 towards Q0528-250, This absorber has an apparent relative velocity that is inconsistent with the Hubble flow indicating motion along the line-of-sight towards the quasar, i.e. z(abs) > z(em). We measure the metallicity of the system to be [Zn/H] = -0.68 +/- 0.02. Using the relative populations of the fine-structure levels of Si II and C I, as well as the populations of H-2 rotational levels, we constrain the physical conditions of the gas. We derive hydrogen number densities of n(H) = 190(-50)(+70) cm(-3) and 260(-20)(+30), cm(-3) in two velocity components where both C I and H-2 are detected. Taking into account the kinetic temperature in each component, similar to 150K, we infer high values of thermal pressure in the cold neutral medium probed by the observations. The strengths of the UV field in Draine's unit are I-UV = 10(-3)(+5) and 14(-3)(+3) in each of these two components, respectively. Such enhanced UV fluxes and thermal pressure compared to intervening DLAs are likely due to the proximity of the quasar. The typical size of the absorber is similar to 10(4) au. Assuming the UV flux is dominated by the quasar, we constrain the distance between the quasar and the absorber to be similar to 150-200 kpc. This favours a scenario where the absorption occurs in a companion galaxy located in the group where the quasar-host galaxy resides. This is in line with studies in emission that revealed the presence of several galaxies around the quasar.