Is there a relationship between rosacea and allergies?

Maybe. Since rosacea can flare after certain food exposures food allergies could be triggers for rosacea.
Probably Not. Acne roseacea is a build up of capillaries on the face and nose. These capillaries can swell and dilate, in the nose, leading to runny nose and congestion. So one can cause the other, but unlikely that both are related.