No — don’t write your CV in all capital letters. Use normal sentence case for your body text. All-caps is harder to read and can come across as shouting, which isn’t the impression you want to make.
Section headings (like EDUCATION or EXPERIENCE) in small caps or bold caps are fine as a formatting choice — that’s different from writing full sentences in all caps.
Quick answer: Keep body text in normal capitalization. Section headers in caps are a style choice, not a rule.