To dream of farting represents issues that are embarrassing to you if revealed around other people. Embarrassing or humiliating mistakes made around other people. Feeling like a embarrassed loser.
To dream of wanting to leave a room to fart in private represents an effort to deal with an embarrassing issue on your own.
To dream of holding in a fart represents attempts to conceal an embarrassing problem. If the fart gets harder to hold in it represents an escalation in your attempt to conceal your problems.
To dream of accidentally letting out a fart in front of others represents an embarrassing information or situations that were revealed to others. An embarrassing lapse of judgement, oversight, or lack of carefulness that makes you look like a fool.