1. Don't pick on me.
2. Don't bother me.
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Are both the same in meaning?
Do you have other expressions which have the same meaning? Do you use #1 frequently?
Again, depending on context ... they could mean the same thing, or they could mean different things.
Don't pick on me = Don't keep finding fault with me or Don't bully me.
Don't bother me = Don't interrupt me or Don't talk to me when I'm trying to read or ...