The picture is suggestive of URTI (Upper Respiratory Tract
Infection) -"Flu" The new development is likely from laryngitis
The cause is more likely to be a virus than bacteria. Secondary infection with bacteria can occur - by then, one will usually have yellow or green sputum
is for bacteria / and has a limited range - you may not need now.
You are likely to benefit from nose drops (decongestant) / steam inhalation and other symptomatic measures
If you don't improve or get worse; if cough
is bringing coloured phlegm, you may need antibiotic - better to see a physician than self medication