It is a serious situation u gotta confront man, you can't live like that waiting for u to get better, the doctors ain't gonna do nothing, they in the situation you got will check the level u have of sickness. Since it is coughing and u find hard to breath, they will probably just give you a medicine to drink or those peppermint candy to open your airways that prevents you from breathing properly. I'm just recommending you to go to the doctors cuz it's worse staying home and wait without knowing if it is serious or not.
The thing is my Aunt says that my throat is probably irritated because my nose is draining fluid into it which can cause irritation
As for breathing Asthma usually fucks around with me for that
Ive been taking medicine but its not something that warrants the hospital yet
My breathing has gotten better after a breathing treatment
Most of the time when i have a cold or covid its like this
Hence why i havent been like- freaking the fuck out (to bad)
As for doctor wise i dont like doctors but i do live with a nurse which would be the one who told me the throat advice