How would you go about removing allergens from a couch?

The best way is to set the thing outside in the bright sun for a few days (but only in the day, not at night). If the innard stuffing is solid, take it out too, and set it out in the bright sun.

That will kill a lot of mold and germs. Then after that, have a carpet cleaning company clean it.

If you’ve been sitting on the couch for two months with no problem, it’s likely something else, but the best way to deal with the problem is to have the couch professionally dry cleaned by a carpet and upholstery cleaning service. There’s anti-allergen and mite products that are part of a dry cleaning process. Have you changed your furnace filters recently?

If you seem to be miserable only when you are home, find out if the previous owners had pets. Its possible your allergic to cats or dogs and just never knew it before. If you get the sofa professionally cleanned and it still causes you to react than you may have to throw it out. If the people had cats or dogs it may be really difficult to get all their hair out of it.
Till then, throw a sheet over it and see if that helps a little.

I’m with @Kraigmo except I’d reverse the process and have the upholstery cleaning done first and then put it out in the sun to sterilize and dry.

I also third the professional cleaning, do you have carpet? it could be the carpet, I have a pretty severe dust mite allergen so I use a special cover for my matress and pillows and get the carpetes and heating ducts professionally cleaned twice a year, you would be amazed at the stuff that is in your vents and floor.

You could also go to an allergist and get the scratch test to see exactly what you are allergic to, that is what I did a few years ago and it has made my life so soo much happier.