Hm. You don't give a lot of details for people to respond to. The answers to the questions you've posed are, yes, of course a submissive can choose her own master. It's hard to imagine it working any other way, although hope springs eternal in the breasts of men who will message you and inform you that you are their slave now. Let me clue you in: no, you're not. In terms of how secretive the relationship would be, that's really up to you and him. I don't know what culture you live in, but if it's one in which women are allowed to choose a dating companion, then the relationship itself need not be secret at all. He's your boyfriend. What you and he do in private isn't really anyone's business.

Sometimes people imagine, and I was one of them, that they want to enter into a sort of "D/s-only" relationship, in which someone is your master but not really your boyfriend. You can try that if you like, although I rapidly found it to be pretty hollow and unsatisfying. If you start a relationship like that, and you still want to do vanilla dating, then I guess the relationship would maybe need to be more secret.