Sorry you are feeling so cruddy for so long. That ER doctor is full of you know what.
Of course Tysabri affects your immune system! It lowers all of our immune systems. There is no way you can see another doc? I think you need to go back for a follow up. The fact that your fever is gone is a good sign.
One thing that might help is some codeine cough syrup -- it will quiet the spasms and coughing and hopefully allow your throat to heal. Also if your throat is closing up and inflamed they can give you a steroid shot (which is usually in the butt I think). I had 2 teenagers with mono in my household and they were given steroid shots to help with the sore throat and swelling.
Make sure you are getting plenty of rest - when you are sick your body just needs more sleep.
I did once have a viral respiratory infection with cough that lasted for more than a month. I want to say it lasted for 5 weeks. And this was long before I had MS and when I was healthy as a horse. It just sounds like you caught a very nasty bug.
I hope you are feeling better soon.