Yes. Time is the natural cure for most pediatric sinusitis. There are some very good recent studies (see by dr. Julie wei) that show clearing of childhood sinusitis by daily saline irrigation of the nose. Most of the time, antibiotics are not needed and are grossly overused leading to antibiotic resistant bacterial infections.
Pediatric sinusitis. By natural do you mean to avoid the use of antibiotic, nasal anti inflammatories and mucus thinners? Ultimately, this would depend on if your pediatrician/ family doc diagnosed your child with a bacterial or fungal sinusitis. Risk of fungal sinusitis depends on what area of the us you live. I would consult with a naturopath with expertise in pediatric ear nose and throat infections.