Can I get a nose job and fix my side profile but keep my front profile looking the same?

Your question has a long answer. The short answer is that you can address your profile without changing the appearance of your nose on frontal view to any significant degree. When you see a rhinopasty surgeon they will help you to understand the process in more detail.

So, essentially, we can adjust the nose from the front or side to your specficiations. I'd recommend smoothing out the side with a more gentle slope and reducing the size of the nostrils.
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Yo may also consider a chin implant at the same time to balance the nose.

Thank you for your question. You are an excellent candidate for rhinoplasty. I think it is one of the most beautifying surgeries that we do as plastic surgeons. In your case, I would also consider a small chin implant. A large portion of my practice is dedicated to rhinoplasty surgery. It is important to only see plastic surgeons with extensive experience in rhinoplasty, ie perform at least 6 per month and have performed hundreds of cases. Also, critically evaluate on-line galleries to see if their art form resonates with yours. Rhinoplasty is definitely a grey haired plastic surgeon's sport. Best wishes to you.