Not sure what isolating does, aside from flooding a room with virus

I realize that isolating/quarantining ensures that you (probably) won’t infect others. But at the same time aren’t I filling this room up with virus? I’m coughing, sneezing, hacking up sputum, etc. and every time I exhale, I imagine I’m shedding virus into the environment. I’m holing up in our tv room, but I’m afraid when I get over this damned covid virus, the room won’t be fit to inhabit. Is there a way to disinfect the place? How long do I need to worry about the dangers of reinfection, or infection of someone else?

The virus persists in aerosol form for up to 9 hours in an unventilated room. You can remove it from the air more quickly by opening windows and getting a cross-current of air going, but if that’s not possible, you can just keep the room sealed for a day or so after you’ve recovered.

If you have a way to get an air purifier, that’s really helpful to keep your viral particles to yourself.

ETA: I got the time wrong for Covid! Listen to @FinsToTheLeft

Most viruses don’t live long in the environment. Aerosolized SARS-COV-19 will survive up to 3 hours aerosolized, longer on surfaces.

Along similar lines, does rebreathing the virus affect your own recovery time? A sick person may expel millions of virus particles per hour. Would purifying the air help the sick person get better quicker since their body would be breathing in fewer virus particles that would need to be killed?

Not really. You have a lot more inside you than what you breath out. Your body has already mounted its immune response and is clearing the body of virus much better than a purifier could.