I was walking down the stairs with my 10 week old daughter and I fell, more like slid on my butt and legs but I think her face hit a stair or 2 on the way down and her cheek is bruised and her eye is swollen, what should I do

Take her to the doctor to make sure she's okay. Being so small that little bruise could be a lot more damage under the skin.

And after this happened, you did not rush her to the ER or your doctor to be checked at once ?

You take her and get her checked.