I would recommend that you contact your doctor and ask if they can recommend an alternative to the Tylenol recommended by Biogen to help combat the side effects. My first dose of Avonex 4.5 years ago produced the worst fever that I can recall having. I called my doctor and stated that if treating my MS with Avonex was going to continue like this, then I didn't think I could do it. My doctor recommended that I try ibuprofen instead. This has worked for me! Early on I would take ibuprofen for about 12 hours prior to my Avonex injection and for 24 hours afterward. I seem to have struggled with side effects longer than the average time period stated in Biogen's literature. The ibuprofen helped a lot, but it still took about 2 years for the symptoms to become trivial. I now only need to take one 600 mg dose of ibuprofen with my Avonex injection to handle the side effects.
As a side note, there was a short period of time a few years back that I took Vioxx to counter the side effects as recommended by my doctor. Vioxx is a COX2 inhibitor which has recently been pulled from the market. One dose of Vioxx completely blocked all of the side effects! I thought this was great and continued for a few weeks until my MS symptoms got worse. I then had someone refer me to a journal article which noted that Vioxx had been associated with aseptic meningitis in about 8 clearly defined cases. This information, along with the worsening of my symptoms, led me to stop Vioxx and return back to ibuprofen. I can't say that Vioxx was directly linked to my worsening symptoms, but I figured that I did not wish to increase my risk of brain inflammation so stopping was probably the best alternative. In hind site, this was probably a good decision especially considering the increased risk of heart attack and stroke associated with Vioxx.
Anyways, contact your doctor as they may be able to help you with the side effects. In addition, there was another post in this section which discussed taking something with an antihistamine to counter the side effects. While I haven't tried this, it may be something else for you to look into.
Good luck, NHE