Can severe allergy cause eye and nasal pain and feeling of nystagmus?

Probably not pain: Allergic diseases do not usually cause eye pain although nasal pain is possible if severe. Dry eyes often cause eye pain but would not have caused nasal problem. See an eye doctor to make sure you don't have glaucoma which may cause blindness if not promptly treated.

Feeling of nystagmus: I think so, yes, but nystagmus is not felt, it is seen. It is important which direction it is. It will be hard for you to see, but a bystander should see it, and a video of your eyes looking forward and in four directions would help someone who cannot see you face to face. Good luck!