This question is impossible to answer very well without having more details about what other medical conditions you have and also what type of surgery
you had performed exactly.
If the type of surgery you had on your nose was cosmetic, then it does seem unlikely that your headaches and dizziness would be related to the surgery.
On the other hand, if you had a sinus surgery performed, then it is possible that you might have persistent sinus congestion, which could conceivably be the cause of your persistent headache.
However, headache and dizziness are very common symptoms in a wide range of conditions, so it is equally possible that they are unrelated to your recent surgery.
I am not sure from your question if you have actually talked to the surgeon
who performed the surgery. If not you should certainly set up a followup appointment with them to discuss your symptoms. You should also schedule a general checkup with your primary care doctor
, as they will be able to perform a complete physical examination and look for other causes of your headaches and dizziness that are unrelated to your recent surgery.