Dear K.,
I have a lot of experience with this one.
I have two words for you.....which your daughter will learn at school when she starts if you don't get her on that track now.....
"INSIDE voices."
It's totally fine to yell and holler and screech and shreak while you're running around the back yard at home, even on the playground at school as long as no one assumes she's being killed or something.....
But otherwise,
In the house, in the store, in church, in class, in the car...
We use our "INSIDE Voices".
Even sometimes, when you are at an outside family gathering, or a bbq or birthday party, even though she is outside, she still needs to use her Inside Voice.
I don't know your daughter but I have known many children like her....I don't think she "forgets" other people are around. She KNOWS other people are around and being loud is her way of making sure they know SHE is around.
The thing you need to express to her is that when she is being loud when it's not appropriate is that people do not listen to her. They are too busy trying to plug their ears so they don't have to hear her at all. The whispering technique works miracles. Start with you and your husband whispering to each other. You can't hear anything anyone is saying if you are screaming your head off. And at that age, trust me, she will be intrigued. Tell her you cannot hear her unless she whispers. Now, she doesn't have to go through the rest of her life whispering or never laughing out loud or anything like that....but you have to let her know that she can whisper what she is feeling and that the screeching is a shut down. The other part of the equation is being sure that you take her somewhere, at least once a week, where she can scream and screech and be shrill to no end and get it out of her system. Then once you get back in the car to come home, it's back to inside voices.
She's 3-1/2, so if you start working on it now, you won't have problems when she starts school. It's possible she would outgrow it on her own, but I know of a kid who was still shrieking in the 2nd grade and she was disruptive in school and no one wanted her for sleep overs or birthday parties. Other parents couldn't take it. And neither could her peers. There was nothing mentally wrong with her. She came from a nice family. But her parents never sat her down and said, "This is really annoying and you have to stop it." She got attention, but not the way she wanted it. And guess what....all it did was make her LOUDER because no one wanted to pay attention to her. And her feelings were hurt.
Try the whisper thing.
Try reading books with her before bedtime in a whisper.
If she shreaks, book is done....lights out. Goodnight kiss. You love her with all your heart but you cannot "hear" her when she is being loud.
It works.