I had rhinoplasty/septoplasty + alar base reduction almost 3 weeks ago. Will my smile completely recover after rhinoplasty?

Muscles that move the upper lip are often affected temporarily by septal and Rhinoplasty surgery.  The associated trauma results in a bruising of the muscle that should resolve  within a few weeks to months.  Because these muscles are responsible for assisting in smiling, the alteration is expected temporarily. 

It's difficult to answer your questions without seeing photos and without knowing exactly what was done during surgery.  Generally speaking, the swelling of the nose after surgery can take many months to subside completely.  This swelling can affect the overall look of your face during animation, so try to be patient.  Please talk to your surgeon and express your concerns.  She or he is the only one who knows what was done and should be able to alleviate your concerns.  Sincerely,Dr. Michelle Spring

Without seeing pictures, performing an examination, an, most importantly, without knowing what was done during surgery, this is really impossible to say.  That being said, it is extremely early for you to start being concerned about the long term outcome.  In my practice, I don't take the first set of postoperative photos for 3 months as it takes at least that long to begin to see the final product.  Talk to your surgeon about your concerns but understand this will likely improve somewhat with time.

It is very common to feel like your smile is "stiff" or "off" and your cheeks are round/full after rhinoplasty. This will subside by 85% over the first 2-3 months, and should return entirely to normal my 4-6 months.

It is best to have an open line of communication with your own surgeon after any surgery to address such concerns.  Others can just guess answers for you. That will not help you.

Reshaping the alar base is going to cause some swelling and some distortion of the lips and the cheeks. This will resolve in another month or two.

Usually the smile is affected because of swelling. This often comes back within about 6-8 weeks.  Be patient.

It is possible to notice a change in smile after rhinoplasty which can be due to multiple reasons, such as placement of tip cartilage grafts, making the tip less mobile with rhinoplasty, alar base reductions, swelling, etc. some of these changes with resolve with time, some may persist for longer. You are just 3 weeks after the surgery, so give it more time for everything to settle. 

It should return to normal. Most likely your smile is altered by swelling/inflammation from the surgery and should return to normal with time (usually within 4-6 weeks). Your smile probably IS forced at this point as you are so early out that it probably is tight and maybe even uncomfortable. Best to discuss with your surgeon as I don't know all of the particulars of your procedure. Your surgeon can be of more specific help. Bottom line is it should be fine.