Smaller Nostrils and Bigger Tip After Rhinoplasty

What you describe is very common after rhinoplasty. The tip appears bigger because the swelling fills it in. The nostrils appear smaller because everything around it is bigger. The whole nose fand upper lip feel stiff because of the swelling.
Swelling usually takes months to go down. Since it has only been 3 weeks since your surgery, you will still have a lot of swelling.
Based on what you have said, and given that I have not examined you, my guess is that everything will be okay.

 It takes 6-12 months for the swelling to go down, so try not to worry about it. It absolutely will get smaller, it just takes time.

3 weeks is too soon to tell what your final nasal shape will be.  Your tip looks big because it is still swollen.  I know it's hard but be patient. It will take a few months before you will see the final result. If you have any concerns, you should definitely talk to your rhinoplasty surgeon. I'm sure he or she will be happy to discuss with you any questions you may have.

Dr. Cat Begovic M.D.