I coughed NONSTOP for the first two and a half months of my recovery. I was very worried that I'd cough the stitches right out, but thankfully, they remained strong and intact.
You've probably already seen this, but in case, here's evidence of my COUGH COUGH COUGH...
The hoarseness took a lot longer to resolve. I think in my case it was reflux induced hoarseness that was made worse by coughing and allergies. I continued to have hoarseness (I was teaching 2nd grade also, which is very voice-intensive. I'm sure that didn't help with the healing. I'm now 2 years retired.). My allergist said to "try not to cough" because coughing does tremendous hard to the vocal chords. Easier said than done, don't you think?
Anyway fast forward three and a half years post-op...I had resigned myself to always having a hoarse voice. Suddenly, the past couple weeks, I discovered that my hoarseness is gone! I can sing again! Hooray! I'm in the midst of allergy season, too, which has always been another culprit for hoarseness.
So...don't despair...healing takes time--in my case, a lot of time!
Hang in there,