After rhinoplasty, a few things can happen which can affect your smile. If work was done at the base of your nose or at the bottom of the columella (skin bridge between the nostrils), swelling in the area can affect the lip and cause it to drop a bit temporarily. As the swelling resolves, which can take months, the lip will return to normal position. Sometime if extensive work is done in this area, the muscles responsible for pulling the uppper lip up are temporarily weakened, a condition which will also return to normal over months. If the problem does not get better by one year's time, you should be re-evaluated by your surgeon.
In some cases, a surgeon may place material between your nostrils in order to provide more support to the tip of the nose. Often this can be a cartailge graft which serves as a collumn to support the tip. A rare complication is this graft slipping forward and down toward the lip. Overall this is a very unusual situation, but if it does occur it can easily be corrected with a minor touch up procedure.
The other thing to keep in mind is that if the tip of the nose is brought up and elevated, it can make the upper lip appear longer. It should not cause the lip to actually drop down and cover your teeth more, however.