At 12 days post operatively from rhinoplasty, significant swelling is still to be expected. It is not uncommon for swelling to be present for several months after surgery, depending on the type of surgery that was performed, skin thickness, implant, etc. Gradual changes in the appearance of the nose may continue for up to one year. Be patient.
I believe that the results which you desire are achievable. Thick skin is not a contraindication to rhinoplasty, nor does it relegate you to having a poor result, however, it is more challenging. First off, I would be very cautious in NOT creating a small nose, but instead concentrate on structural stabilization of the cartilage of the nasal tip and at the mid vault. A proper septoplasty would also contribute in helping straightening the nose and resolving any nasal airway obstruction that may be present. The size of the ala can be addressed with a conservative alar base reduction or Weir resection, taking care not to cause a secondary problem such as an external valve narrowing or collapse.