One Nostril Not Healing Properly After Rhinoplasty

The pictures seem to show that the incision of the alar base reduction on the left has split open. Such a problem is not "normal" and should be evaluated by your surgeon.
I would be leery of closing a dehisced wound at this stage, though, since the swelling could make it hard to precisely close the wound edges and the contaminated nature of such a wound could increase the likelihood of infection by closing it.
A reasonable approach for such wounds can include simply letting it heal in on its own and then revising the resulting scar--often a minor in-office procedure--several months later.
All the best,

--DCP

It would be my advice and opinion to let it heal. An attempt at closing this "open" is not generally a good idea because one it is open, it may have a higher chance of becoming infected.
Letting it heal on its own with Neosporin as your doctor advised is a reasonable alternative. In the event that this produces excessive scar it can be revised at a later date when the risk of infection is low. Attempting a quick fix now may not ultimately give you your best result.

Hi Poli,
It looks like the Weir incision made to narrow your nostril has opened.  It needs to be sutured.  If closed properly you should not end up with the "horrible scar" that you are worried about.  Good luck.
Dr. P