I once watched some American TV show, and there was a guy, who just woke up, and he said: "I need to brush myself up". It was clear that he was going to go to the bathroom to take a shower and etc., but I didn't manage to find some examples of using that idiom that way, is that really common phrase? Or was that kind of slang or something? I know only "brush up on something".
I'm American. I've never heard that. I've heard, "I need to brush up" or "I need to go brush up," which means, "I need to brush my teeth." People often say this in the morning because they often wake with bad breath or with a bad taste in their mouth.
The verb phrase "brush up" in the above sense is intransitive, not reflexive, so you wouldn't ever say the reflexive pronoun "myself" with it.
If you click that link and scroll down to "brush up," you will see it is transitive when it refers to refreshing your knowledge about something and so can take an object like "myself," albeit it requires the addition of the preposition "on" if you do. Without "on,: transitively, the object is what's being reviewed (e.g., "I'm going to brush up my writing skills," albeit "I'm going to brush up on my writing skills" is also correct.). So, my point is, you're right about that. Saying "myself" with "brush up" denotes refreshing your knowledge or memory by reviewing related materials.