I Have a Red Dot on my Bridge, Will This Go Away After Rhinoplasty? (photo)

Looking at the photos provided, the red spot appears to be due to an abnormal collection of fine blood vessels near the surface of the skin. This type of abnormality is separate and unrelated to the underlying structure and shape of your nose. I would disagree with the opinion rendered by your rhinoplasty surgeon that it will go away as a result of the surgery. Reshaping the nose would have little effect if any on the blood vessels in the skin. This would require evaluation and treatment by a physician versed in managing this type of skin condition. This would like involve use of a laser that can specifically target the blood vessels. 

This appears to be a vascular malformation such as a spider angioma that can be treated either with a laser or very fine electrocauterization. It is unlikely to improve or disappear with a rhinoplasty so don't depend on this being a solution. What you can do is undergo a rhinoplasty to improve the appearance of your nose and if this is still present after surgery, later on you can have it addressed with one of the 2 above mentioned techniques.