Long story short, you should not have blurted that out and no, your character does not know everything you know (nor do you know everything your character knows). That is exactly why intelligence skill checks exist.
Intelligence checks exist to resolve uncertainty as to the outcome of a character attempting to recall lore or make deductions when there's a meaningful consequence for failure. They have no bearing on what a character may think (which the player has absolute authority to establish), except as the player decides.
You should have said something like, “Does that name mean anything to my character?” and your DM should have called for an Intelligence (History) skill check. If you fail that, then as far as you’re concerned she’s an elf lady in a floating chunk of earth.
Given the above, in my game it would look more like "I try to recall the significance of that name, drawing upon [some past experience and/or training] to see if this is someone we can trust." If the outcome of that task is uncertain and there's a meaningful consequence for failure, then I will ask for a check. If I did ask for a check, the failure condition might be something like "she is an evil lich of some renown... and the expression on her face suggests she knows you know it."
If I was your DM, the fact that your entire party is now conspiring to kill this character based entirely on meta game knowledge they shouldn’t have would immediately cause me to make her an innocent elf who is just trying to help you.
I would never do this as DM. In this instance the DM set the stage for "metagaming" to occur and some DMs would then demand the players don't "metagame" in the face of that. Changing things to thwart the very "metagaming" the DM encouraged is not the way to go in my view. The problem - if it can even be called a problem - is easier solved upstream by reminding the players that assumptions can be wrong and that the smart play is to verify one's assumptions before acting on them.