Yes, there are asanas that can help sinus problems, such as sinusitis and the pressure that results. Sinusitis is an inflammation of the nasal sinuses. The sinuses are hollow pockets of air located on either side of the nose, behind and in between the eyes and in the forehead. The sinuses produce mucus that cleans and moistens the membranes of the nose and throat. Each sinus has an opening into the nose that allows for free exchange of mucus and air. Sinus pressure, as your student has experienced, results when these openings get plugged. As mucus and pressure build in the sinuses, the sinus membranes become irritated and can swell and become further blocked. Then there is danger of bacterial growth. An acute bacterial infection needs treatment, either with an antibiotic or some nonallopathic treatment.
Allergic sinusitis can be controlled provided a consistent yoga practice is maintained. Yoga practice helps both in the moment (at the time of practice) and cumulatively, so a regular, daily practice is required if your student is to get lasting relief. However, if the amount of allergen is above a certain limit, no treatment will completely help, be it medicine or yoga. It may take time for nature to eradicate the allergen from the body.
Practically speaking, several poses are invaluable for relieving sinus pressurenamely, standing poses; Sarvangasana (Shoulderstand), done on several rolled mats arranged from the shoulders to the elbows; and Ardha Halasana (Supported Half Plow Pose). Sarvangasana and Ardha Halasana should be held for some time to receive the full benefits. The sinuses may remain blocked at first; but after some time in the poses, as the practitioner relaxes, the sinuses usually open up, bringing relief. Eka Pada Savarganasana (Plow Pose with one leg up and one down) is also particularly good: The inversions act as a natural flushing mechanism for the blocked sinuses. The blood circulates with tremendous force into the stagnated areas, clearing away the secretions to clear the passageways and restore free breathing.
Practice Headstand only after the disorder is alleviated. At that point, regular practice of inversions helps keep the sinuses and respiratory tract healthy.