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In this scenario, the statement indicating a potential complication is the client's report of coughing up foul-tasting, brown, thick sputum. This symptom suggests the possibility of an evolving infection or the presence of an abscess or necrosis in the lungs, which can be associated with complications arising from pneumococcal pneumonia, such as an empyema or a secondary bacterial infection. The nature of the sputum—foul-tasting and brown—implies that it may contain pus or necrotic tissue, which is a departure from what would typically be expected after starting antibiotics.

Other statements from the client, while noteworthy, do not specifically indicate complications related to the treatment of pneumonia. A sharp pain in the chest during breathing could suggest pleuritic pain or a side effect of the pneumonia itself but isn't as directly indicative of a serious complication as the sputum change. Sweating all day might be a sign of a fever or infection still present, and feeling hot off and on could suggest fluctuations in fever related to the condition, but these statements do not point to a significant change in the status of the infection as clearly as the sputum change does.