Why does swollen turbinates cause head pressure & tightness in the head?

Sinus congestion? The swelling undoubtedly involves all the linings of the nasal cavity, including sinuses, not only the turbinates. It's just that the turbinates are easy for the doctor to observe. Your "head pressure & tightness" probably are due to general congestion including sinuses. Try a decongestant spray like Afrin®, then discuss with your doctor if it doesn't help.