My nasal bones are wider after rhinoplasty. Is this common, and if so, what causes it?

As you are only 3 weeks
post op. It sounds like your nose is swollen. Swelling can take many months to
subside and swelling does make the nose appear bigger. It is best to see your
surgeon and see if he will suggest tapping your nose?

At three weeks you are likely still very swollen. At this point you need to give it time to heal. This can take 6 months to a year.

Unless your surgeon performed an osteotomy intentionally widening the bones, you are probablu experiencing some swelling of the upper vault.  This should improve with time.  See your doctor for an exam to be certain.

The splint you were wearing not only held the bones in place, but kept swelling out of that compresswed part of the nose. With the splint off, and your activity level increasing, you probasbly have more swelling in the nose. The bones are unlikely to separate, but to be safe, check in with your surgeon.