Can impacted/rotten wisdom teeth cause swollen glands & throat tightness with dysphonia at times? Increase reflux symptoms?

YeS! If not able to clean, wisdom teeth can get infected by oral bacteria (cavity). This infection can spread into the salivary glands and glands below the tongue. These glands can swell, causing difficulty swallowing. Trying too hard to swallow can cause reflux symptoms. Get those infected teeth out! A dental problem can become a medical problem very quickly if they are not removed.
Yes. You should be examined. Your immune system will be slightly suppressed in general with persistent pain from malpositioned wisdom teeth.