Poor airflow. Some ways that this could happen include having persistent congestion or nasal polyps that could interfere with airflow in your nose, even after recovering from a sinus infection. You may need a ct scan or a rhinoscopy to better understand why this would happen. Also be aware that some antibiotics like biaxin (clarithromycin) can alter your sense of taste temporarily.
For the last week or so I've had a taste in my mouth I can't seem to get rid of it taste like when I have a sinus infection, but no other symptoms?
Bad taste. Bad taste can come from various sources. First get a thorough dental exam. If there are no dental or oral problems, check with an ENT specialist. Smoking, diet, acid reflux, and drugs all can cause taste problems.