Stiff Upper Lip After Closed Rhinoplasty?

It is very common for rhinoplasty patients to report (in the first several weeks after surgery) that their upper lip feels stiff and that it is difficult for them to smile. Fortunately, this resolves by itself in the first several weeks after surgery as the swelling subsides. Be patient, your smile should return to normal.

It takes 6-12 months for the swelling and stiffness to resolve. If it does not show signs of improvement , return to your surgeon.  

If you had your tip projected with a columella-strut, immobility of the central lip is common, and resolves in around a month. How long ago was your operation?
I don't have any personal experience with "detachment of the depressor muscles", but my hunch is that your upper lip will be fine with time. What does your surgeon think?
Best regards.

After rhinoplasty the upper lip can
sometimes feel stiff and difficult to move as a result of swelling. Rhinoplasty
always results in some degree of swelling as this normal healing, and swelling
at the base of the nose can result in stiffness in the upper lip.As the swelling improves the lip
movement and sensation will return to normal. The likelihood of stiffness is
dependent on the rhinoplasty surgery, revision surgery with multiple grafts are
more likely to result in an increased degree of swelling and resulting
stiffness. The symptoms improve in most people within a few weeks however
rarely up to 6 months. 

This is not in usual with a rhinoplasty, particularly when depressor muscles operated on. A sharp instrument is used to separate the depressor muscles from their attachments to the bone at the base of the nose. This in itself will cause swelling which will limit lip movement ,as well as the actual separation of the muscles will limit their contraction. As swelling resolves and the muscles reattach, things should return to normal. The nerve that contracts the muscles could also temporarily be affected and this could also cause stiffness

 Stiffness  of the nose is normal after a rhinoplasty. This may take 6 months to a year for the stiffness and swelling to subside. Your smile should come back to its usual form.