Is there a connection between allergies and sinusitis?

Yes. Allergies can lead to sinusitis in 2 ways: 1) allergies cause inflammation of the sinus membranes and inflamed membranes are more easily infected than "normal" membranes. 2) allergic inflammation causes swelling of the drainage tubes from the sinuses causing a build-up of pressure, mucus, and bacteria which cannot drain from the sinuses and therefore results in an infection.
Yes. Allergies can cause excess fluid in the sinuses and nasal passages. This fluid creates a place for bacteria and viruses to grow, creating sinusitis.