What can be done to fix my side profile?

I'm not really clear what you mean by "droop down in a recessed way", but I can tell you judging purely on those photos, it doesn't need 'fixing', because it isn't broken. If you are very unhappy about your profile, you might want to have an in person consultation with a qualified plastic surgeon to explain your concerns in detail, to see if it could potentially be changed (not fixed!) to something you prefer.

I believe you are referring to your chin which is vertically long but horizontally short. A sliding genioplasty that brings your chin forward as well as vertically shortens it as it comes forward will change both adverse chin dimensions. Computer imaging can show what effect that type of chin change will create on you.

What can be done to fix your side profile? According to widely accepted aesthetic norms your nose would be considered to be slightly over projecting and your chin, slightly under projecting. Some surgeons might recommend a Rhinoplasty to reduce the projection of your nose and a chin implant to increase the projection of your chin. But this is all a matter of taste.

Hi and welcome to our forum!
From your photos, I note that you appear to demonstrate a high nasal bridge. This can be improved by undergoing a closed rhinoplasty, where the elevated portion of the bridge is lowered by removing excess bone and cartilage. The nasal bones are then mobilized to narrow the bridge itself to prevent an "open roof" deformity. You appear to be an excellent candidate.
Visit a board certified plastic or nasal surgeon for evaluation and discussion.