I am recovering from a sinusitis (2weeks), and have hardly any nasal congestion, but my cough doesn't go away. I'm exhausted?
Partial recovery. You may only be partially improved. Depending upon your anatomy sinus infections can sometimes require longer courses of therapy. Sometime antibiotics need to be changed. Also, sinusitis can trigger asthma. The asthma can make you cough. Sometimes antibiotics used to treat sinusitis cause stomach upset and laryngeal reflux which also can make you cough. I recommend you talk with your ENT doctor.
See a pulmonologist. The fact that a so-called sinus infection has resolved but the cough lingers is most likely a viral infection. About 98% of adult upper respiratory infections are viral; antibiotic treatment of a cough is rarely indicated unless your cough results in the production of a purulent (pussy) discharge, which could be cultured and treated. When a cough is persistent, i advise seeing a pulmonologist.