Nose injections and septoplasty.

A septoplasty will address your deviated septum and improve your breathing.  This usually does not change the outside of your nose and therefore fillers can still be used to make any aesthetic changes.  Also, you may need surgery to address the external appearance as fillers may not be adequate.  Based on the complexity of your question, the best answer is to see a facial plastic surgeon for an evaluation.

Your question addresses two different complex issues that you are considering.

First, if you have breathing problems through your nose, a full examination by a surgeon is essential to determine where your breathing issue is coming from.  Commonly, a deviated septum can narrow the inside of your nose and restrict your breathing.  A septoplasty is the standard treatment to straighten your septum.

Very often, a surgeon can offer you a rhinoplasty in conjunction with your septoplasty.  Since your nose will already be operated on, it is convenient to do additional work on your nose at that time.  A rhinoplasty can help straighten areas of the outside of your nose that you feel are crooked.  This is a good, permanent treatment.

Filler injections are a good tool for the "non-surgical rhinoplasty."  They can help straighten or provide augmentation to certain areas of the nose.  A few disadvantages to filler injections to the nose: 1) they can treat only specific types of issues and are not always a good option in all patients, 2) they are temporary and need to be repeated on a regular basis to maintain the result you are looking for, 3) there are certain risks to injecting filler in the nose that, in my opinion, make it imperative that you are injected only by a facial plastic surgeon or plastic surgeon who is an expert in the nose.

To truly know if you would benefit from a filler injection to the nose vs. a rhinoplasty, I recommend you visit a surgeon for a full consultation and evaluation.

Best of luck!