getting a girlfriend isn’t about being dominant, even if being charismatic usually would be helpful, it’s also not required

you shouldn’t feel pressured to get a girlfriend unless you want one, and you certainly shouldn’t be pushed into a relationship on someone else’s terms

I don’t think you should feel embarrassed, but I would understand if you felt angry - your autonomy is being violated, and ironically your dad is only enabling and promoting the behavior he seems to be judging you for. Either way, I’m sorry you were put in this situation, you shouldn’t have to deal with this.