Can sinus pressure be the cause of my vocal nasality?

Hyponasal speech...: can be due to nasal and sinus congestion. Swelling inside the nose due to the common cold or allergies or even a sinus infection can lead to less air flow through the nose resulting in a nasal voice (hyponasal) as if you're speaking while holding your nose shut. Sinus pressure can also be due some of the above causes, so yes you may have both symptoms as a result of nasal congestion.