Are you sure about this, with Covid?
Repurposing the mucolytic cough suppressant and TMPRSS2 protease inhibitor bromhexine for the prevention and management of SARS-CoV-2 infection
The decision to put a person on a cough suppressant is a doctor's decision, IMO. There is no blanket advice. There is no way to cough coronavirus out of your lungs once it's there, and there are doctors who believe the irritation to the lungs from coughing is beneficial to the spread of the virus within the body - and so they order cough suppressants. This is especially true early on in the illness. University of Maryland Medical has a recommendation to use cough suppressant for Covid up on its website. Personally, I would use it and while I have heard this advice about coughs being good for the process of disease, I am a strong doubter.
Medicines that fight COVID-19: What to know
Same thing with the fever (which can use up precious somatic energy, especially if the person is experiencing chills, which can happen with fever as it approaches 100°. Again, my doctor has said for us (DH and I) to use tylenol if we have even a mild fever. She's UCLA-based. She's not alone in this advice. (See the link just above - where the medical news aggregator reviewed the literature and says Tylenol (Acetaminophen) is a front line medication for Covid-19, especially when there are chills and fever.
The idea that we are supposed to let fever rage out of control as it "helps kill" viruses is not true in Covid-19 and it may be the opposite. At any rate, no one should trust internet strangers on this - that's why choosing and consulting with a concerned and educated primary care physician is so important. My colleagues and I all have different doctors, and we compare notes on what they've been telling us daily.
But tylenol and cough suppressant are in my coronavirus toolkit, hopefully won't have to use either. I too used to believe in this "no suppressant for coughs" business and when I told my doctor that on my first visit, she just stared at me. She said it wasn't the front line thing to do for my cough (allergies) and prescribed a new allergy med for my nose (worked, no more cough) but she was very concerned that my respiratory tract was constantly irritated and I think I can see why.
Here's a website that offers methods for cough treatment aside from suppressants:
How to Treat a Cough from Coronavirus at Home
(Humidity not only treats the cough but also helps bring virions to the ground, thereby reducing viral load in the area; zinc lozenges at the first hint of a sore throat/cough are also beneficial). My colleague's physician said humidifier would be a reasonable first line of defense in their household (with an immune-compromised person and 2 kids).
And here's a good, balanced summary regarding the "suppress" vs "let it ride" fever debate:
Fever: suppress or let it ride?
The article cites a study in which tylenol had no effect on eventual mortality in hospital-based virus treatment (2015, so not the current coronavirus) but did keep people out of the ICU for a longer period of time. The jury is still out on whether fever is adaptive or maladaptive and probably depends on the specific pathogen to some degree.
At my age, with pre-existing inflammatory conditions, my doctor says to go ahead and take it if fever is approaching 100°. Your doctor may say differently, depending on age and other variables.
