The answer is different in different offices, since there is no data that directly answers your question. My opinion is that kenalog (steroid) injections bring down swelling and limit the deposition of scar tissue. If overdone, they can thin the skin/soft tissue envelope and cause distracting depressions, or alterations in the quality and drape of the skin. But in my experience that is rare.
I consider an injection as early as one week post op, typically in cases where its a revision and I know the patient has a tendency to heal with a lot of scar tissue or skin thickness.
More commonly I wait until one month post op. By that time some of the swelling has resolved and it's easier to see where a steroid injection has merit.
I also have four different concentrations for the steroid we inject, in order to further control how aggressively we are manipulating the healing process. So because of that, I use it quite a bit in my practice. I have to back that by noting more than one of the leading educators/surgeons in the rhino world use kenalog on every rhinoplasty one month post op.
Two things specific to your situation. One, revision rhinoplasty always swells longer than the original rhinoplasty. Two, open rhino swells more than endonasal rhino. And the tip (or infratip lobule) always holds the swelling the longest