To find Millicent in Elden Ring you are going to need to head to Caelid and get through the Town of Sorcery. Here location is here on the map.
She is sitting at the church and it is guarded by some of the bug people. If you go inside and talk to her she will tell you to stay away. Offer her the needle and she will use it on herself. It will heal her, but she will pass out for now.
Head to the Shrine of Grace and use it. This should make her wake up and you can talk to her again. She will say it worked and she feels much better. You will get an emote (I believe? I forgot) and she will say she might take a journey now. After she said that I came back and she was gone. I will update if I come across her in the world again.