First of all, it's important to know that everyone's face has numerous asymmetries if you look hard enough and analyze enough. One nostril attachment will look higher than the other in anyone who smiles asymmetrically -- and most people can and do smile asymmetrically, at least some of the time. So the point is that others don't notice that nostril asymmetry nearly as much as you do and if they do notice it, they don't think about it or their mind interprets it as being due to a normal asymmetric smile. So don't fret about that too much. It's a very difficult thing to fix without producing significant scarring at the base of the nostril.
As for the size of your nose, the problem is primarily in the lower half of the nose, and plenty can be done about this. Both the tip of the nose and the total width of the nostrils are proportionately too wide, and can be narrowed using common rhinoplasty techniques. However, the difficult part is to narrow the nose while keeping the profile looking ideal and all other angles looking natural and normal. That's why it's so important to find a surgeon who can demonstrate, through multiple before and after photos, that they do consistently excellent work. Without that proof, you are taking your chances.