Yes, they all three have the same overall meaning. In formal writing you would most likely write "I just have to see for myself" or "I've just got to see for myself ". "I just gotta see for myself" may be used as well, but gotta is informal of "got to". Also, depending on the circumstances (of how formal the situation is) contractions such as "I've" may be frowned upon (contractions are not typically seen as professional to universities, etc., at least in my experience).

I just gotta - is just more "cool"/style for a song. In a conversation formal AND informal you would say "i've just got to". Hope this helps