Moving to a new city can be difficult on the sinuses. Chiropractic can be helpful by allowing the neck and related musculature to move and function correctly, thus allowing the sinuses to drain better. If you are wanting your sinuses drained, it is best to see an Ears, Nose, and Throat (ENT) doctor.
For long-term relief, go to your local farmers market and grab some raw honeycomb (sometimes grocery stores have them) and chew on a piece of it like gum daily for a few months. This will help your body be exposed to a small quantity of the allergens that are present in your area (make sure the honey is from within 15 miles of your house) and allow you build up a resistance to them.
A chiropractor can adjust the upper neck to help with this, but won't drain the sinuses directly.