Jess,
Here are some thoughts I typed up after healing from voice surgery (mine was with Dr. Haben).
For relieving cough, he actually recommends gentle throat-clearing (the 'impatient' sound) as opposed to coughing or swiftly moving air. He also recommends
warm tea with lemon and honey as the overall best cough suppressant - the prescription stuff is only for the desperate. Ideally, you want raw, unfiltered honey - it will say this on the package and the honey will not be 'clear' or translucent. Manuka honey is the gold standard. Do not add it to hot tea! Let the tea cool for several minutes until it no longer feels hot to the taste at all, then add the honey. This will preserve the healing properties of the raw honey at their optimal level. Likewise, a half of a fresh squeezed lemon will be more beneficial to your healing than the preserved stuff in a bottle. (This is culinary therapy! Treat it as such.)
Immediately post-op I did have significant phlegm, which I was able to clear by just exhaling with a little force. I did my best to only gently clear the throat a few times as needed. I had no full-blown coughs at all. As you're waking up they gave me ice chips to suck on, which I highly recommend. Constant, small sips of something warm or cold really helps suppress the urge to clear mucous. I also had the strong urge to burp, but recalled that HouseHippo had issues with this, so I resisted just in case; and it actually went away without incident on its own before I left the hospital.
If you're going to be out and about a lot, I highly suggest having a handheld noisemaker - I never actually needed the bicycle bell I bought for this purpose, but you want some way to rapidly communicate the equivalent of a "Hey!" on a second's notice if needed.
Get the following apps for your phone: "Speak" and "Megatext". You can queue up phrases in each as needed (note - Megatext won't let you use punctuation unless you upgrade). Be sure to test different voices and speeds in Speak so you can be understood clearly. I tried them all and found "(English) Nicky" with pitch at ~1.15 and speed at .45 was easy for others to understand. If you have a bluetooth speaker for your phone voice to speak through, you'll be in great shape
Early in healing, I actually didn't really get random urges to cough (as opposed to just clear my throat) except for a few moments in days 3-6, since the sensation of the suture in the throat became a little more of an irritating than an "oh, right, that's there" tickle, but light sips of honey lemon tea seemed to help. I could also feel the vocal folds move a bit if I yawned, sneezed, or was holding back laughter (all unvoiced of course), so I did my best to suppress those functions. In week ~3 there were a few minor coughing fits, but it wasn't a big deal.
