Is she just 3 or nearly 4 ? Because if only just 3 then I'd say quite a lot of it is normal and a lot of it is boundary testing - so you need to be firm with boundaries, and frustration at not being able to have her own way all the time (toddlers are all about Themselves
)
With tantrums - within the limits of where you are, just walk away and let her get on with it (assuming she can;t hurt herself) be deaf to screaming.
And again with the party situation, be firm and matter of fact 'it's this prize or no prize' continued screaming 'OK it's no prize' and leave even if she is kicking off.
Not walking - 'then we're going home if you are to tired to walk' if you are with your DH then he can pick her up, he's bigger than her, it doesn't matter if she insists on it being you, he can pick her up and she can yell if she likes.
Somewhere she has decided that screaming gets her what she wants (your undivided attention, and her own way) so you have to reverse that - if she screams or is rude she gets neither of those things. If she is polite and well behaved she is more likely to get what she wants.
And enormously praise behaviour that is good. So if she does ask for something politely, show her you appreciate it, and if she walks tell her she's a good girl for walking nicely etc etc. Praise wherever you can. be firm and matter of fact (without raising your voice) over anything unacceptable.
Just repeat 'No we are doing XYZ' and don't move. You'll find if you can keep calm and not get angry (Easier said than done obv !) you won;t feel so out of control and miserable. And you being in control with give her a greater feeling of safety and knowing what is what.
When it comes to it, children don't like being out of control emotionally, they like boundaries.