Okay, I'm interested in this kink too but I know very little of it and haven't tried it at all (the missus isn't into anything rough).
What I CAN say to you, though, is; "is this safe?" - NO! This is a form of what's known as edge play because, putting it bluntly, it carries inherent risk that cannot be eliminated completely and, if something goes wrong, can end in death. Scary but true.
There are safer ways to do it, sure, but it will never be 100% safe. Ever.
Now, it sounds like you have some minor damage/bruising to the larynx, which means it was done "wrong". One of the things I've heard is that any FRONTAL pressure to the larynx and hyoid bone should be absolutely avoided, they are very fragile areas and any lasting/permenant damage is very serious and, as I said, potentially fatal.
*From what little I've heard on technique; A hand can be placed high up on the throat, just below the jaw, and light pressure can be applied UPWARDS (towards the face/head), and fingers can apply very light, gentle pressure to the SIDES of the neck. Pressure should NEVER be applied from the FRONT or DOWNWARDS (towards the back of the neck/spine). These can mimic the sensation of choking, and trigger the response in the brain, without actually cutting the oxygen off completely, and without damaging the larynx/hyoid.
*Please, please, please don't just go off my very limited, possibly inaccurate information on technique. Do lots and lots of research, ask on Fetlife and such for info from seasoned practitioners, take it very slowly, never do it alone, etc. I just wanted to point out that basically a tender larynx means minor damage has been done and isn't right. If the tenderness/pain doesn't get any better or gets worse in the next couple of days, or you develop any other symptoms, you may need to go to A&E.
Have fun, but stay safe (or as safe as it's possible to be with edge play)!