Can Swelling of the Columella and Tip Cause a Tip to Look More Upturned?

Yes, the initial swelling of the columella and base of nose can temporarily push up the tip. This should settle down in the first few weeks after surgery, if it does occur.

Three weeks post surgery is still very early for you to judge the results of your surgery - especially in the tip/nostril region

It is very common for the nose to look more upturned (rotated) than it really is. This is particularly true during the first two weeks following surgery because of the degree of swelling in  the skin of the nose. Also, some patients expereince swelling of the upper lip in the area immediately below the columella (column of tissue between the nostrils).  When this area swells, it can distort the angle of rotation  and make it appear that it is tilted up more.

Be patient, this should improve with additional time. Discuss your concerns with your physician.