Yes you are over-reacting but it is understandable so don't worry
Children get bitten/bite quite a lot, it's part of growing up and getting used to being around a peer group as opposed to with their parents.
That's not to say this is something that should be taken lightly, just something that should be taken with the appropriate level of concern.
It is the nurseries job to manage this and your job as a parent to make sure that they are looking after your child.
The questions I would be asking are:
1) Is the biter a serial biter or was this a first offence?
2) If the answer to (1) is "they've bitten before" then are they biting lots of children or targeting your child?
On the basis of those answers you can ask them to a) move the biter or b) move your child or c) do nothing but keep an eye on the situation.
(c) is almost ALWAYS the right answer as this is just part of growing up.
Please don't take a day off and sit with your child, you can start some horrific patterns in early childhood that, literally, take years to grow out of if they feel that every time they hit an obstacle mummy will rush in to the rescue. They might like that and we may feel needed but it is a sure fire highway to hell.
hope this helps