I now have productive cough with yellow sputum in addition to to sinusitis with post nasal drip and loose stools What is the likely cause

The short version: your symptoms point to a respiratory infection, but the loose stools are a separate clue that changes the picture.

Your productive cough with yellow sputum plus sinusitis and post-nasal drip fits acute bacterial sinusitis, where Streptococcus pneumoniae and Haemophilus influenzae are the most common culprits [1][3]. But the loose stools complicate that. Antibiotics commonly cause loose stools as a side effect [4], so if you are already taking one for the sinusitis, that is the most likely explanation for the diarrhea.

If you are not on antibiotics, the combination suggests a viral respiratory infection that has spread to the gut, or a separate gastrointestinal issue entirely. The retrieved studies focus on sinusitis treatment and do not address the cough-plus-diarrhea combination directly. That gap matters: no study here tells us how often these symptoms travel together.

The evidence on sinusitis treatment shows antibiotics help only modestly. About 1 in 7 to 1 in 18 people improve faster with antibiotics than without, while adverse effects run around 27% with antibiotics versus 15% with placebo [2]. That means roughly 1 in 4 people on antibiotics get side effects, and loose stools are among the most common [4].

My call: if you are on antibiotics, the loose stools are likely drug-related; if not, this is probably a viral infection affecting both respiratory and digestive systems. Confidence: moderate, because the retrieved evidence does not directly study your symptom combination.