Yes allergies can cause some peoples noses to burn which is normal.
Once the allergies go away the nose should stop burning but if not then you should see a doctor.
Damaged or diseased sensory nerves in your nose can also cause your nose to have a burning sensation so if your allergies go away and the nose still burns then something else could be wrong.
But if you suffer from seasonal allergies then the nose burning is normal and nothing to worry about.
Once your allergies go away then the burning sensation of your nose should go away as well.
To help with the burning sensation of the nose during allergies make sure to drink more water, use a humidifier in your room and also use a saline nasal spray or allergy nasal spray to help clear the nose.