What do you do when your boyfriend is talking inappropriately to another girl?

I have been with my boyfriend for 9 months. He started a new job (which I supported him in taking) where there were a lot of females and recently I have begun to get a bad feeling about some of his interactions. I told him my concerns and he said that I was being jealous for no reason. I told him then that to me, an emotional affair would be just as bad as a physical one. He said that I should trust him and that he would never hurt me like that. We rarely ever have sex and it's always been that way. The excuses started with not feeling good about himself because of financial troubles and so forth. Now he's telling me that in addition to that, me trying to get him to have sex (I make a move about once a month), and me being worried about other girls, makes him not want to. I have been working so hard not to be jealous, and have stayed quiet even when things do bother me. He recently left that job, and before he did, two single girls took him out to lunch, which I said nothing about. This week, still feeling insecure, I stooped to checking his phone and found messages between himself and one of those girls. He wrote her on valentine's day to thank her for a gift (which I knew nothing about) and that it would always be very special to him and that he was thinking about her on valentine's day. They have been writing back and forth and talking about not losing each other, and very much wanting to see each other. She also said that she has kept a wall up because she would never do anything to intentionally hurt someone's relationship but that she is really looking forward to seeing him. I think the fact that she is saying this is intentionally trying to hurt our relationship. From the tone of the messages, it certainly feels like there is more than feelings of friendship between them. I have been working so hard and he has made me feel so bad about questioning him and all of this has been going on. I love him but is it worth it? Am I being overly sensitive? Should I tell him I know about this? Help please. I am hurting big time.
What do you do when your boyfriend is talking inappropriately to another girl?
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