Wow... I've been going crazy trying to find ppl online with this same exact issue... Luckily, I found this thread...I thought it was rare but I guess it's not at all.
Like most of you I noticed this with a double mirror. I'm currently 22 and started noticing this assymetry a few years ago (3-4 years).
What I notice of the right side of my face is the following:
1) Right side of face looks different than left side
2) Looks and feels flat
3) Feels like there's less bone density
4) My hairline is uneven, gets higher from left to right.
5) Makes my hair look uneven
6) By the temple, I feel a kind of bulge.
7) Jawline looks longer

Cheek is very flat.
This affects my self-esteem a lot. If my right side looked a lot more like my left side, I'd be a lot more confident and happy.
I've been researching this for over a year now and the only doctor/surgeon that is remotely close to dealing with this type of problem is a Craniofacial Surgeon.
I've seen some recommendations of Oral-Maxillofacial surgeons, but I think Craniofacial Surgeons are more specialized since they deal with extremely severe deformities of the face and skull. At first I thought my issue wasn't bad enough for a Craniofacial surgeon, but there's nothing else that comes close to this assymetrical problem.
I was told CAT scans of the face is the only thing that can really prove anything.
Consultation fees range from $100-250. I'll be visiting one this month hopefully.
This information should be helpful!