You cannot raise your voice and you cannot "go off" on your boss. Being childish and unprofessional will never help your cause.

What you are describing is not typical unless the dating peers are causing more work for everyone else or acting unprofessionally. Look really hard at your behavior.

Otherwise, you need to have a conversation with your manager. Tell them you make a conscious effort to keep your personal relationship with your gf out of work, and the only issues seem to be coming from otherl employees. Say that you checked company policy and there are no rules against dating as long as you're not in each other's reporting structure. Tell them the negativity and being watched all the time is making it difficult for you to carry out your job duties. And that you'd hope if there's an issue with your job performance that would be addressed, but you'd like your personal relationship to not be a topic of conversation moving forward.

Meet with your manager on your own, not with your girlfriend. And speak for yourself, not your girlfriend.

Stop flirting and showing affection at work.

Only spend time together at work when it's professionally necessary, except lunch, etc. Even doing your own thing then would be good. That helps keep things professional, allows you to have your own work lives, and keeps coworkers from realizing you broke up if that ever should happen.