I want to mouth "what the fuck" to my girlfriend
Why is that? Has your girlfriend done something to deserve being sworn at?
Yes, she hurt my feelings and embarrassed me in front of her family and friends.
While it's good to tell your partner when they are doing something upsetting to you, and it might be best to be discreet about it, in this manner. However, you should always be respectful to your partner or otherwise they will become angry and upset in return at your behavior, especially if you use swear words (even silently). If you feel your girlfriend has embarrassed you in front of others and hurt your feelings you should discuss it with her calmly and constructively so that she is more receptive and willing to address the issue.
F*** you, you don't know a f*** thing about relationships.
I know from my own experience, and the experiences of many other people, that reacting with anger and profanity almost always has bad consequences. I also know that trying to be calm, and to let people know how you feel tends to be much more effective. I hope that you are willing to give this a try, and if it doesn't work, you can always try something else.