E.,
I've had a lot of experience with biters, and I have found that there are typically two types- the one who has something to say and not the verbal skills to get it out, and the one who simply needs a lot of sensory stimulation. Does Ellie have a lot of words to express herself? Even still, when she is frustrated, does she have a hard time getting her needs met (i.e. "that's MY toy" or "I need more space"). Sometimes toddlers need us to help them figure out when they need to be alone- but they can't tell us that! You could introduce sign language to help her out- it wouldn't replace her current vocabulary, but it could help her when she can't think of the words (she could wave byebye long before she could speak, right? so signs are easy.)
The sensory tot could have been the baby who put absolutely everything in her mouth, loved to feel different textures, trying loud noises and soft, etc. Try offering her a variety of things that stimulate her senses each day- KoolAid playdough (bright, smells good, feels great!- email me if you want the recipe!), paints, music, crunchy foods, etc. Watch for overstimulation, though, and respond to her cues.
Since she's only bitten twice, check to see if she's teething (2 yo molars) and give her appropriate things to bite ("We don't bite people! We bite apples (or this chew toy)") BTW- you're doing a great job having her help you tend to Michael, but maybe instead of putting her in time out, try having her stay with you as you tend to him. She will see the full process of soothing him and tending his "wound". At her age, she doesn't have the capacity to stay in time out thinking about what she did, so keeping her with you shows her what you want her to think about- that Michael is hurt and that she did it. Use words like "Ellie bit you! That hurts, doesn't it?" You're not trying to shame her, just to show her that when she bit, she hurt her brother (which she doesn't quite understand- she knows she got a big reaction, but not how much it hurt him). Tell Ellie you didn't like that!" coming from Michael that biting hurts helps reinforce it- "Don't bite me, Ellie! That hurts me! Use your words!" And of course, it helps to know WHY she bit so you can give her the words she needs for that situation. Good luck! Biting, although unpleasant and scary, is very common. And a good playgroup facilitator would be happy to help you through this phase, and preschool will help further. Don't panic!