I'm of the definite opinion it could be the Avonex precipitating your depression. Here's an interesting case study (about Rebif, another interferon) Depression and Suicidal Ideation in MS
We report a case of depression and suicidal ideation in coincidence with the start of increased doses of interferon beta-1a and their complete reversal following the drug withdrawal.
My experiences don't exactly match Rachel's but I've definitely concluded the side effects of Avonex in my case last about 4-5 days. You'll note the case study mentions increased "irritability". When my colleagues chide me about whether or not I took my "nice" pill on any given day, I usually say, "No, but I shot up last night."
IMO the capacity of interferons to precipitate depression in people with MS shouldn't be underestimated. I haven't switched to Copaxone yet but I'm definitely thinking about it. Sorry about your job....that can't be helping.