Hanging Alar and Columella? (photo)

In general, your ala will retract and lift up slightly as you continue to heal after rhinoplasty.  You have a moderate amount of swelling in your nose, and it's too early to make any conclusions about the final result.  You may find that as the swelling resolves your symmetry and alar-columellar relationship also improve.  

The shape of your nose is going to continue to change as you heal.  It's too early 2 months after surgery to begin worrying about a revision.  Follow up closely with your surgeon, let him/her know your concerns, and give your nose a chance to heal.  

The amount of swelling I see in your nose is normal at two months after rhinoplasty and would encourage to be more patient.  

You are correct that you do have thick skin of the nasal tip.  This thick skin will definitely blunt the type of result that you desire.  However it has only been 2 months since your surgery so relax and give it time and you may see some nice change to your nasal tip.  It can take up to one year for all of the soft tissue swelling to resolve.  

You have very thick tissues, and you are only two months out from surgery.  Give it a year for the swelling to go down.