You seem to be having rhinitis. The primary symptom of rhinitis is a runny nose along with sneezing, watering of the eyes, congestion of the nose and itchy nose, throat, eyes, and ears.
You are right in saying that steam inhalation is beneficial in rhinitis. Along with steam inhalation, you can take nonsedating antihistamines like cetirizine (Zyrtec) or loratadine (Claritin).Moreover decongestants and topical decongestants may help in reducing congestion of the nose.
You can use eucalyptus oil or products containing menthol with steam inhalation. This should help.
Pls visit your physician if the condition persists for a longer period.
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