"Brush oneself up" is a common phrase?

Solution 1:

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.