Will Alar Rim Grafts Make my Nostril Sidewalls (Which Are Very Thick) Look Thinner?

I would have to see the photos of what has been done previously and what tissue remains. Alar rim grafts are done for "pinching" of the tip, not thick walls.

Alar grafts are used in nasal reconstruction to fix over resected alar cartilages.  Over resection is a common post rhinoplasty issue.  This can contribute to alar retraction and collapse of the nasal valve when you breath.  The grafts are used to help restore the natural strength to the ala.  Typically, grafts are harvested from septal or ear cartilage.  Then these are not available other types of cartilage may be used such as rib cartilage.  This more cartilage in the ala, it will naturally be thicker which is generally welcome.  Rather than doing a lot of on line research, you would most likely benefit from seen rhinoplasty surgeons with good reputations in consultation to see what they think.  Be aware that both general plastic surgeons and facial plastic surgeons perform rhinoplasty and it is the surgeon not the credential that makes for a good surgery.

The optimal relative proportions are left-right cheek nose junction distance equal to the distance between the inner and outer corners of an eye. Usually this is 32mm. The distance can be larger if the nostrils are bigger or the nostril rims are bigger (than the usual 3 to 5 mm) or some combination of these 2 causes. The procedure for correcting depends on what is causing it. If the nostril rims are thick and the nostril size is normal it is better to thin the fat in the rims than to try and bring the rims closer together. Without photos, face to face examination, knowing exactly what surgery you had etc. it is impossible to say what your current condition is or what should be done about it.

The most important thing for you to do is get copies of your photos and operative report from your medical records so that if you see another surgeon it will be much easier for them to know what is going on and what needs to be done.

My response to your question/post does not represent formal medical advice or constitute a doctor patient relationship. You need to consult with i.e. personally see a board certified plastic surgeon in order to receive a formal evaluation and develop a doctor patient relationship.

Without seeing you or at least pictures, it is hard to tell. It sounds like you have had external Weir incisions to reduce the base width. There is a practical limit to that procedure. If over done. the nasal base takes on a box like configuration and breathing can be impaired. I don't think  alar grafts as I understand the question would help

Alar rim grafts will more than likely provide stronger support to the alarl rims, but will more than likely make them thicker rather than thinner.