Common for right-handed surgeons to make septoplasty incisions along the left side of the septum
One of the most commonly used incisions during septoplasty is called the hemitransfixion incision. For a right-handed surgeon, it's much easier to manipulate the septum when this incision is made on the left side of it. It may be difficult to visualize, but the surgeon can access both sides of the septum through this incision and most surgeons always make this incision on the same side, regardless of the side of deviation.
With that in mind, the reason for your persistent breathing issues may be due to a number of factors, though residual septal deviation and persistent turbinate hypertrophy could certainly be the culprit.
You do have a slightly increased risk of developing a septal perforation with revision surgery, but certainly in experienced hands this risk should be minimized.
There Is No Wrong Side Septoplasty
As some of the other surgeons have noted, there is no such thing as performing a septoplasty on the wrong side. While you may not have seen improvement after surgery, it does not have anything to do with which side incisions were made on. Revision septoplasty can be undertaken but I would also look into the possibility that you have some other nasal functional problem, such as alar collapse or internal valve problems, as about 20% of people with septal deviation need additional procedures to get optimal results.
Unlike your eyes, you only have one septum
In your body there are many paired organs; eyes, ears, lungs, kidneys etc.... Surgeons can and have operated on the wrong one. Not so for you septum. Its not possible to operate on the wrong side. You have naturally assumed since the incision is on the opposite side of your deviation and the deviation appears unchanged, the wrong 'side' was fixed. Instead you have had a failed Septoplasty. Unfortunately that happens, but its not malpractice, nor even poor surgery. Every surgery has a failure rate and with Septoplasty its in the range of 20%. Go back to your surgeon if you still have trust and talk about what the next step could be.
The septum is a midline structure. There is no right or wrong side for the surgery. It all depends on your surgeons "entry point."
Now, a poorly performed septoplasty can result in no improvements of the septum or even make the septum worse. That is a different story. But it has NOTHING to do with what side the incision is on. There are many different incision types for a septoplasty.
The turbinates are a different story. Ask him to see which side he reduced. often it is done on both sides. You most likely will not be able to see any incisions for the turbinate reductions.
Don't get angry but do ask him what he did. Revision septoplasty can be difficult depending on how much of the cartilage and bone was removed.
I do not have an answer to the persistent obstruction, but the septum is a mid-line structure. I personally make an incision on both sides, but many right handed doctors operate though the left side only. That does no mean that the doctor operated on the wrong side.
Talk to your surgeon about the perceived persistent obstruction which may disappear after six weeks or so.