I went through his phone and found out ambiguous texts. Does it count as cheating or what?

I came from a broken family where my father had several affairs during his marriage with my mother, so it gives me a trauma of having difficulty to believe in men, or, believe there is someone in this world that will love me truly.

Previous relationships are always ending bad because my possessiveness and jealousy.
Starting a new relationship beginning of this year, i was going to start fresh, no snooping or jealous at all. I really tried.

In the beginning was good and easy, but when the honeymoon period has gone, i started to get anxious. Once he went out to buy something and left his phone with me, I snooped. I didn't find anything bad, so I felt secure.

It's like an addiction, I did it again. While he was having shower, I snooped again. I found he was texting other girls, and apparently I can tell from the texts that he's trying to know more people in a sexual way.
I didn't tell him, I hold my concerns, and kept silent.
There were times we discussed about honesty and loyalty, he said he will never cheat on me. And we both agreed that cheating is not only physically but also emotionally, that means both agreed not flirt or "look for" other people during our relationship.
Few weeks and months went by, I was still anxious. So I took a chance to look again.
This time, I found he was texting all those girls all the time, including his ex, there's one girl in particular seems really close to him, because they use the terms like "i miss you, I love you..." and send kiss and hearts emoticons.
When I asked him indirectly have you been "looking for" or "flirting" with other people or your ex, he said no. I asked again and say can you look me in the eyes and tell me the truth, he did look at me and said he didn't. He said: it's a horrible thing to do! So what is it now? Does it mean he is trying to stick with his lies and bet that I'll never find out? And he's just gonna denying that forever?
We're gonna move in together next week, I'm so stressed.. HELP!!
I went through his phone and found out ambiguous texts. Does it count as cheating or what?
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