My heart hurts

I have a girlfriend whom I have been with for almost three years. We have a good relationship and I Love her and our family more than anything. I am an alcoholic in recovery and have been sober for 4 1/2 years and as a consequence, do not have many friends. i usually just look forward to being with my family for my social needs. Recently, however, my girlfriend got a new job and made new friends. She mostly befriends males, which make me feel a little jealous I'll admit. She has one friend in particular, I'll call him Z, that she talks about and texts frequently. I question the motive of her friendship with Z and she assured me that they are just friends. Over time, I began to feel more and more uneasy about the nature of their friendship. She never did anything like stay out all night or lie about her whereabouts, but they talked (texted) far more frequently than before. I kept asking her about why they need to communicate so much but she only responded that they are friends and Z was going through some difficulty. i broke down and read her texts and saw her giving flirtatious messages and even saw a message stating. "I'll dream of you and me". I confronted her and she revealed that since having our baby, she doesn't feel pretty and this guy was interested in her so she embellished it. I knew that she had that low self esteem since the baby and always try to do something special for her and work hard to try and make her feel sexy and pretty, but apparently she wanted to feel that way from others as well. I said that this not only hurts me and makes me feel extremely insecure (most of my past serious girlfriends, though I was not sober at the time, had cheated on me). She assured me that she would lay down the boundaries of her friendship between her and Z, but they still go out at work, text all the time, and of course she is far more guarded about her phone. I respect her privacy, so I don't want to be a snoop, but it is hard when I feel so insecure. I don't know how to communicate it to her without being repetitive and it frustrates her when I ask if she doesn't want to be with me or what her and Z are always texting about. I'm really hurt and uneasy about this relationship and sometimes feel like giving an ultimatum to choose her family or her friendship with Z. I realize however that she needs her own set of friends but this particular relationship makes me feel very threatened. Please give me any advice to help me deal with this situation. Note: my girlfriend does assure me that she only wants to be with me and loves only me, but it's hard for me to believe when her actions seem to display interest in another person.