I too have this problem..
My 3/4 profile from my right side is not too bad looking, my eyebrow looks nice, the skin is tighter, less acne, my nose is straight, my eye opens wider, my cheekbone is more pronounced..however..the 3/4 profile on my left side is just an uglier version. I have more acne, the skin seems to be lacking elasticity, my cheekbone is barely visible, my eyelid is a lot bigger, my nose has a bump, part of my lip is lacking pink pigment on my left side as well...I always used to think that my right side represented all my good attributes and my left side represented me when I'm feeling a little nervous or awkward or whatever. I've been reading online stuff and it tells me that that can actually be true, which is super weird...It drives me insane that I look different from both sides, I just wish I'd have a symmetrical face..It doesnt even matter if its the ugly side of me just as long as both sides would look the same. I also feel super self conscious when people are talking to me on my left (ugly) side and I try to avoid sitting to the left of people...I think about this TOO much, and lately I've been trying to find the good in my left (ugly) side because I know what I'm doing to myself is not healthy..The only advice I can give you is work your ugly side and pretend its your good side...I've been trying to use the same kind of energy I have when I'm talking to someone on my left (ugly) side as when I'm talking to someone on my right (pretty) side. It's sort of helping...I guess blabbing about it on this forum isn't helping the problem go away, but I just wanted to let you know you're not alone out there. Its a horrible problem and I've also showed my family but they just say I'm crazy...I dont believe them. but...I'm totally agains't plastic surgery so I guess I better start getting used to it, right?
This goes for me as well: don't worry too much about it, it's worse in our heads because we spend so much time in the mirror analyzing it. Try to accept and forget about it and hopefully one day we will be able to appreciate both sides of our face!!