Flu for 6 days, still have a fever fluct between 38-39.5C. Not improving much. Tight chest, mild cough. Could it still be pneumonia without bad cough?

Possible. Did you have influenza diagnosed with a flu test or are you just assuming from symptoms; By 6 days you should start to feel better eventhough cough can hang on for 2 weeks or so. Pneumonia can be a complication of influenza. You should be seen especially if you were not seen initially for these symptoms.
Unlikely, but. Pneumonia as a complication of influenza is less likely in a young heathy adult, as compared to those over age 65 and people with a chronic medical condition. Although most people feel better in a week, some will be symptomatic for 2 weeks. Though less likely it's best to call your doctor for advice.
Be watchful. Its not unusual for flu symptoms to last this long. But if you have productive cough and shortness of breath or if you have underlying conditions like asthma, COPD, or immune suppression disease or therapy (like for cancer or IBD), etc. then get checked. Hope that helps.
Possibly. Have you seen a physician, had a flu test or a chest xray?- time for an examination. Never ignore a febrile illness.