Asymmetrical Rib Cage Due to Pectus Excavatum?

Nothing beats face to face consultation wIth a fully accredited plastic surgeon. Your asymmetry is not necessary to treat so first decide how much it bothers you!

If you truly have pectus, then it is a good idea to have a consultation with a thoracic surgeon. If it is not causing physiologic issues, then most would not try to fix a mild deformity.

Thanks for your photos.  I do not appreciate the marked difference that you do but that being said, if you wished to improve symmetry without implants, consider fat grafting, assuming you have a little extra somewhere else.  It does come with risks so you must be willing to accept that as well.  If you have excessive fatty tissue above your right breast, you could even consider liposuction to diminish the prominence you appreciate.  You need to see a local surgeon who can help guide you through this.

I would get an opinion from a chest surgeon who has experience with correction of pectus excavatum.  If you are not interested in a prosthesis there is not much else that can be done at the present.

I am having a tough time seeing either a pectus or any noticeable asymmetry on the posted photos. Photos are helpful, but not comparable to an in person evaluation where a three dimensional view is evaluated. 

Since you have exclude implants, the remaining technique that might be appropriate is fat grafting. A consultation with a plastic surgeon is the way to find out what options you have. 

All the best.