Is it cheating?

I saw in my boyfriends phone that he had gotten a bartenders number (the bartender at the local bar in town) we just moved so we just started going to this bar. I guess he has gone more often than me, like on his way home from work and just told me he was still working. So I saw the conversation and he was asking about her friend, saying "do you think she will like me? Can you send me a pic of her? Can I have her number?" Then he said he hasn't seen her in over two years. So I guess he knows this girl. And this girl is supposedly the bar tenders best friend. Then later on in the messages he starts hitting on the bartender saying "you're a good girl and there's not many of those left...if only you were single lol...etc etc" and then he said sorry I just meant that as a compliment I don't want you thinking I'm a jerk because I'm really a great guy. And she said "well I think you already know what I think of you so no worries, that is a compliment". My heart sunk when reading these because it's happened numerous times in the past. I see him talking to hikes and then when they ask about me (bc they've clearly seen me with him) he says "oh she's not my girlfriend she's just a friend, she wants to be my girlfriend but I don't like her like that". As if we HAVENT been together for 3YEARS, DONT have an apartment together, DONT talk about marriage and having a family etc. our relationship was bad in the past but within the past year I saw a huge change in him and I saw how much more he showed me affection and I really felt like he changed. He told me it took some time but he finally realized I was the one and he wanted to spend the rest of his life with me. I really fell for it this time. I flipped out on him and he said he didn't cheat, he said I'm over exaggerating. He said he didn't even call the girl once the bartender gave him her number. He said it was more of him just wanting to see if "he's still got it". Well he's 35 and I'm 22, I think he's still got it!!! I'm sorry I'm just so upset and I don't want to vent to anyone I know. I just feel like I'm in shock because I really thought that he would never do this again. What do I do?? I want to leave and stay by family for the night, but in afraid he's going to go to the bar or have a girl in our apartment. I have bad anxiety as well so that doesn't help. But I lost all my trust that I gained for him and now if I were to stay with him, I would want to see his time sheets, look at his phone every day, never let him go back to that bar without me, Etc. and I've lived like that already and I'm tired of it. It's not how a relationship should be. I love him so much and he makes me happier than anyone in the world. He's like my best friend and I've never felt so comfortable with anyone else. He's the first person I've ever let my guard down with, the man I lost my virginity to. I've been 100% faithful this entire relationship. And I just feel that my confidence level is extremely low. I feel like I'm not good enough because if I was, he wouldn't be wandering. I do so much for him. I work full time and study full time and then come home and do the household chores each night because he works and wants to relax when he gets home so I bust my butt so that he can do that. He helps me too but I just feel like I am always putting him before myself. Naturally I do that because I love him so much. So when this happens it's a huge slap in the face. I can keep going on and on. Thank you to whoever reads this. I really needed to vent