Swollen tip after rhinoplasty. How drastically will my nose change after the swelling?

You are correct in that you're very early in the healing phase from a rhinoplasty. The entire nose is likely still somewhat swollen. The nasal tip is known to have persistent swelling after rhinoplasty for weeks to months in comparison to other regions. Without seeing photos it is difficult to comment on the swelling, however, it will likely decrease with time. It is imperative that you followup with your rhinoplasty surgeon throughout this process because they may be able to manage some of the swelling in the office with steroid injections and/or nasal taping maneuvers. 

While a lot of swelling will go down in the first 3 weeks or so, it will take 3-6 months for all of the swelling to go away, followed by contraction of the skin for another year or longer.  So don't worry too much now as things will likely improve a lot.