Can he be cheating?

Hello everyone I neex advice.

My boyfriend and I have been dating for three months at first everything was wonderful. I caught him texting his ex in thr second month when she had text him. He said he was trying to be petty which doesn't make sense. I text back and to stop texting that he had a girlfriend. After that we didn't have any problem. Recently last week he went to this kids party and he refused for me to go. So i called him and i told him I know it's because she's going to be there anx he said well I don't know if she is or not but they said she wasn't.

Anyways, after that we still see each other. However, he is too tired to have sex. I do know that he is working longer hours. However, it doesn't make sense before that day our sex life was very active. He says I'm over thinking but I domt know I'm confused. Can he be cheating? He said his not talking to her but it crosses my mind that he is cheating.

He seems faithful but I can't forget the fact that he was texting her? They were together for 3 years until she cheated. Or relationship was great until that. I dont know what to do? He denied it and just say he is tired. Can he really be tired? Or can he be cheating?
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I don't know what to think? Like I said he has been working longer hours.

And the text messages was just like how have you been? Nothing big. She was the one who had contact him. But it still hurt me that he was replying. I feel kiie if i would never found out. He would have continue to text? Other than that we have a great relationship.
Can he be cheating?
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