Irritation in your nose is called rhinitis and it leads to increased mucus production which can then go on to cause a runny nose, post-nasal drip, a nagging cough, and sinus inflammation and fullness. When it's due to allergies, it's called allergic rhinitis.
What is an allergy? Basically it's your body responding to what it sees as a foreign invader and is usually a very small particle. I want to focus on allergic rhinitis because we are having some really high pollen levels right now and probably will be for a while due to all the rains causing such good plant growth. And if you want to monitor it for yourself, here's one spot you can do it.
People tell me all the time "I don't have allergies". Well here's the thing - yes you do. We all will if the concentration of an allergen is high enough. Otherwise it means your body isn't doing it's job. There are some people who are much more sensitive to low levels of allergens and those are the people who we typically think of as having seasonal allergies, but depending on the season, it can affect all of us.
But, there's actually not anything too harmful for the most part about the pollens in the air and the reaction your body gets is a little bit of an overreaction so it's helpful to try to tamp that down a little bit with medications.
The ones that are probably most effective are nasal steroid sprays like Flonase (fluticasone) and Nasacort OTC (triamcinolone nasal spray), both of which are over-the-counter. The nasacort sometimes works better for people because it's not alcohol based. The other great easy option is an oral antihistamine. Zyrtec (cetirizine), Allegra (fexofenadine), and Claritin (loratadine) are the ones that aren't supposed to make you drowsy. I hear our allergists recommend zyrtec more than the others but in theory they all work about equal. Stronger stuff like Benadryl (diphenhydramine) is more effective but also more likely to make you sleepy and people over 65 can sometimes get confused and have bad falls when taking it.
As far as natural remedies, there is scant evidence that locally-sourced honey can be helpful, but it's mainly been studied in people also taking antihistamines and the amount you need to take is pretty high (about 1 gram per kilogram of your body weight) so I'm not a strong proponent of it.
Here is some more information for you about nasal allergies, a.k.a. Allergic rhinitis and how you can help control them. I encourage you to listen to the podcast on "Managing Allergies" as well.