Yes. In general infections can increase the heart rate depending somewhat on severity.
The heart accelerates the rate at which it beats so as to facilitate the circulation of oxygen and immune cells which are needed to initiate the healing process.
md-health
The blocking of nasal passages will make you breath more rapidly to avoid oxygen starvation, the heart rate will also increase for a similar reason.
Medhelp Posts
Sinusitis can narrow or block small arteries that can cause an increase in heart rate as the heart tries to compensate.
Steadyhealth