Are sneezing and itchy nose just symptoms of allergic rhinitis?

Specific symptoms. Sneezing and nasal itching are very specific for allergic rhinitis while nasal congestion and post nasal drip occur with virtually any nasal condition.
Probably. Sneezing, runny nose, nasal congestion can be seen with viral infections and non-allergic rhinitis but if your nose and/or eyes are itchy it makes it more likely that your symptoms are due to an allergic reaction, that is, allergic rhinitis (rhin = nose; itis = inflammation; so rhinitis = nasal inflammation).

Related Questions

How do I know if I have alergies and how can I heal it I have a runny nose, itchy nose, and sneeze?

Allergies? Get checked out by a doctor. Could be from allergies. This can usually be helped with medication. You may need allergy testing to help make the diagnosis.

What should I do if I have a runny nose, itchy nose, and sneeze and I have a spray called nasonex (mometasone) will it help?

Yes. Yes, Nasonex (mometasone) will help with your rhinitis symptoms, you need to use it as directed, it will take a few days to kick in, you may also use an over the counter saline nasal spray in addition to help with your symptoms.
Runny nose. Most allergies especially seaonsal types respond well to nasal cortisone sprays such as with nasonex (mometasone). Only for short period of time as directed in the instructions.