Overly flirty boyfriend??

Savannah • 19, from Dublin, Ireland. 😁🍀 Design student @ NCAD 👅
Im 19, and so is my boyfriend. We've been together for 2 years now, and since he started his new job I've noticed he's very flirty when talking to other girls, I love him and I do trust him but it bothers me because I know of it was the other way around he would flip? I don't know what way to show him how much it bothers me and I definitely don't want to do it to him, what should I do? 
Also one of the girls in work he has kissed before a couple of years ago. And a couple on months ago he called me another girls name when he was drunk/asleep so I checked out his phone to find out he had told a girl he was in college with that he really liked her, I comfromted him about this and he said it was nothing it was when we were going through a bad patch and he feels nothing towards her, I believe him but this is making me nervous about him being flirty with other girls? I don't know what to think... 

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