How can I stop myself being so jealous about my boyfriend texting other girls?

My boyfriend and i have been together for over and a half but recently he has started talking to a girl 9 years younger than him who has just started in his work. I think that he is only doing this to help her to feel secure in her new job however how often they text is upsetting me as we were on holiday a month ago and they were texting silly things a lot and the conversations usually began with a question about work and led on. He is a bit sick of my paranoia and we have decided that we shouldn't look at each others texts anymore but that makes me more jealous as i'd prefer to know what's going on. If i question him too much about it i think it will finish our relationship and from what i know we have a good relationship and haven't really had any bad patches so far and i'd hate to lose him. Should i ignore the issue and hope she stops the texting soon or ask to see the messages? It wouldn't bother me as much if they didn't work togther and i think because of the age gap nothing would happen but i can't be sure as this has never happened in our relationship before. I should also say that having female friends doesn't bother me it's just girls who begin to speak to him that concerns me. Please help. xxxxxxx