Your vocal cords need to be able to respond in a nuanced way for singing, especially for "healthy-but-challenging" singing. If they're puffy due to illness or irritation, most of us won't be able to hit high notes effortlessly and in tune.
Do you ever find you have a tight or gravelly voice when you are otherwise healthy? First thing in the morning? After coffee? After pizza? After being exposed to an allergen?
If your voice feels at all tight or gravelly, that's a sign that the vocal cords may be puffy, to some degree, and for most people, this means they may not be able to perform the way they should for effortless high notes.
One of the biggest causes of "puffy cords" is reflux. Reflux is contents from the stomach and/or lower intestine, in the form of liquid or small areosolized particles, that enter your esophagus and travel up toward or beyond your larynx. Heartburn is a form of reflux, but many other forms of reflux go largely unnoticed, or manifest in the form of other maladies such as post-nasal drip, or asthma, or "coughing at bedtime," etc. Or, for singers, it can manifest in something as subtle as a feeling that singing isn't as easy as you remember it being at some other point in time.
Reflux matter doesn't need to make it all the way to your vocal cords for your brain to sense something is wrong and tense the muscles in your throat, so effortless singing becomes difficult. Convesely, it can make it all the way past your esophagus and condense on your vocal folds, causing swelling.
Mainstream medicine generally treats reflux by giving sufferers a long list of foods to avoid, and prescribing over-the-counter antacids or stronger medicines called proton pump inhibitors (PPIs) which limit stomach acid production and can reduce the symptoms.
The problem is that PPIs have been through many systematic reviews of the studies, and have repeatedly been shown to have no benefit over placebo in randomized double-blind studies. For references on this, check out All About LPR by Thomas F. Lee, and Heartburn Cured, by Norm Robillard. There are some studies that show a small benefit from PPIs, but there are other studies that show that PPIs make things worse, especially when patients stop using them, as well as in study participants who took PPIs even though they had no reflux to begin with--they developed it upon stopping the PPIs.
Norm Robillard, the author of Heartburn Cured, is a PhD microbiologist specializing in gut bacteria, who was also a 20-year uncured reflux sufferer. One day he went on a very low carb diet with his son, for weight loss purposes, and within two days his reflux was gone. In his books, he lays out his hypothesis that many forms of reflux are likely caused by gas from the bacteria in the lower intestines; specifically bacteria that thrives on sugar and other quickly digested carbs (starchy vegatables, all processed carbs such as anything involving flour/pasta, and white rice). This is one anecdotal account, but one can search and find many instances of doctors who have been successfully treating reflux by prescribing carb-restricting diets. Carb restriction for reflux treatment has a few studies behind it, but not a lot of solic clinical consensus. That said, you just need something that works for you, now, and it should be easy enough to try carb reduction for a few days without any health risks for most people. I suggest reducing carbs and "trying not to eat too much" in general for 4-5 days, if you are suffering from reflux, and seeing what effect that has.*
Dr. Robillard also hypothesizes that PPI meds may create further gas from the small intestine, by limiting stomach acid, which causes the fats and proteins which would normally be broken down in the stomach to instead need to be digested by the gas-producing gut bacteria.
Either way, he believes gas pressure in the small intestine forces its way up into the stomach, and from the stomach up into the esophagus and sometimes beyond.
Another piece of the puzzle was suggested to me by Dr. Reena Gupta, an LA-based laryngologist, who pointed out that the breath control demands of singing can mean unusually rigorous pressure from the diaphragm on the stomach and the valve muscle at the top of the stomach that typically stops refluxate from entering the esophagus. In other words, if you have excess gas pressure in your gut, but it isn't causing reflux, singing could actually be the tipping point that causes the reflux to occur.
I'm not really advocating either form of treatment, here. Feel free to try mainstream medical treatment, or limiting your carbs, or both, but try being mindful as to what seems to increase and lessen reflux--I'm for whatever works.
I have a lot I want to say about how to sing well, in coming posts, but it's all moot if your cords are swollen--much of the coordination of great singing just won't be available to you with puffy cords. I know this won't be an issue for everyone, but I felt it was important to mention first, for this reason.
Let me know your thoughts and experiences with reflux in the comments, and happy singing!
*I am not a doctor and am not qualified to give medical advice. Any diet modifications you choose to try are at your own risk and should not be undertaken without the supervision of a doctor.