Do I have alar rim retraction? Will it go away on its own? (Photo)

Generally six weeks is too early to determine if the slight alar rim retraction you see on the left side is permanent.  There is a lot of swelling in the top of the nose at this point which can distort things.  You need to continue to follow up with your surgeon and if, at a year, there is still retraction then you should consider having it corrected.  Generally alar retraction will occur with excessive cartilage removal and in the photo you submitted it does not look to be the case.

I agree that you have asymmetric nostrils with the left having a notched or retracted appearance.  While you heard correctly that the nose will take up to a year to completely heal, it's very unlikely your retraction will get better.  One of the challenges of rhinoplasty is despite the best efforts of surgeons, your nose may heal and scar in unpredictable way.  Swelling and tip refinement are some common things that will get better with time. However, contracting scarring typically won't reverse itself.  The best advice is to maintain good follow up with your surgeon.  I'm sure he/she will also want to follow your healing.