Tatiana, thanks for the photos and detailed description. You have accurately described your asymmetries, but have come up with an entirely incorrect "reason" for what you see.
You have focused on your right breast as having the problems, and obviously prefer the feel and appearance of your left breast. It does appear as if your right breast lift may have been slightly "looser" than your left, but by your photograph and description, I believe you may actually have a capsular contracture on your left side, whereas your right breast pocket is not contracted, making it feel "soft, squishy, and like a sack of mud." I believe you meant to type your right breast is flatter than the left, which also goes along with some degree of capsular contracture on your left side (or at least a smaller submuscular pocket).
It is extremely doubtful your implant is ruptured, but a "tantrum" is a pretty colorful term for your surgeon's response. I am sorry if one of our colleagues has responded to you in this way, as your issues are real, correctible, and pretty "standard" for a full breast lift plus implants in a fair number of patients. If your surgeon is unwilling to discuss the revisional surgery that is recommended to address your concerns and improve your symmetry, you may need to see one or more other ABPS-certified plastic surgeons for advice.
You may also want to be prepared for advice about surgical revision on the left side in addition to, or perhaps instead of, surgery on the right, since soft is more natural, even though higher, tighter, and more "perky" can be an unwitting outcome of capsular contracture on your left side. The best compromise in your case may be additional skin reduction (tightening) on your right side, possible capsulorrhaphy (internal pocket sutures to tighten the pocket), and perhaps a higher profile implant on that side if you are adamant about not releasing what is actually unnatural firmness in your left breast.
Unfortunately, unless you wish to travel to Europe to see my friend Dr. Verpaele, polyurethane-covered implants are no longer available in the US, but can indeed minimize the recurrence of capsular contracture in appropriate cases. The presently-available cohesive gel implants (by either manufacturer here in the US) are excellent products that are exceedingly durable and cannot leak and rarely rupture (would require a major force such as a car crash or severe injuring blow to the chest). This is NOT an implant issue, it is a tissue issue (sorry). Good luck and best wishes!