they can mean cheer up, like if someone is crying, you may say either(or Pull yourself tgther), or calm down, like if someone is upset or angry/ out of control, you could also say them. Basically they both mean, to control your emotions...
cheer up is correct. Put yourself together means you are all crazy and your not your self and so put yourself together to show your still the same person. And get a hold of yourself means your running somewhere but then you feel so wrong that the person your using is doing something you don't usually do so get a hold of yourself and find the real you.
both of them may be right
From what I've understood in using these two phrases is that "get a hold of yourself" is usually used when someone is really upset, mainly because your mind is running all over the place with thoughts. Imagine it like a person having 3 other bodies, going in all different directions. Then someone tells you to get a hold of yourself and to calm down.
The other; "put yourself together", I would use also as a calm down because again, it's usually used when someone is upset, but I would picture it as someone who's been crying or emotionally upset in some way and then to face the world, needs to "put themeselves back together".
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