There are a lot of issues here. Right off the bat, I'm going to recommend marital/relational counseling. Seriously. You made a passive/aggressive move. You planned to purchase a phone without telling her because you KNEW she would not approve. Instead of talking it out, which would risk your ability to control the outcome, you chose to try to take matters into your own hands.
To some people, the 200 needed to purchase the phone means nothing, as they have plenty of money to handle it. To others, it is a big deal. To your GF, it's a big deal and you should have honored that and you didn't. To her, the question is: how and why should I trust him going forward? He's secretive.
I don't give this relationship much hope if it isn't built on trust as relationships that ARE built on trust have plenty of troubles to start with. I've been married 31 years. I know the end of this behavior. The problem isn't with the X it's with the relationship.
Therefore, since this post has nothing to do with the X, imo, I am moving it to a more appropriate place. The Lounge.
Again, please consider counseling, if you care about continuing to live with your GF and your baby.
Rev. Steven58 (ordained minister)