Xylitol nasal spray (XLEAR) is commercially available OTC for treatment of rhinitis: http://www.xlear.com/xlear-sinus-care/
However, most of the published studies focused on xylitol nasal irrigation rather than nasal spray. The studies with small with 20 to 50 patients each and the results were mixed. The references are below.
As of year 2019, xylitol nasal spray (XLEAR) and irrigation are not the standard of treatment for chronic rhinitis and sinusitis.
PubMed search: https://www.ncbi.nlm.nih.gov/pubmed/?term=xylitol+nasal