Severe electrical problem in my 98 Chevy Cavalier?

[Sara]

I knew I had a slight electrical problem with my car when I bought it because I noticed my headlights would dim on and off slightly. Last night the roads were icy and it was dark - some deer ran out in front of me and I had to slam on my brakes to avoid hitting them. This caused my anti-lock brakes to freak out - When I continued on my way my headlights were now flashing on and off rapidly and it seemed as if my cylinders were misfiring? I'm sure they weren't actually misfiring but some kind of electrical connection was certainly not reaching the point it was supposed to. I was close to home so I slept on it. Drove during the day today and I could still feel the loss of power when I would accelerate (as if it was misfiring). Drove again tonight and the headlights are still flashing on and off. I am at a complete loss as to what kind of electrical problem this could be and how to even start trying to fix it. We did a test on the battery and the alternator and both seem to be working as they should. I'm just completely stumped and need this problem fixed asap! This car is my lifeline!