anxiety about cheating

My boyfriend of 6 months was making comments that alluded to him cheating in passing a month ago for a few weeks. I talked to him about it and he quit making the comments. He also has absolutely no problem hitting on girls in front of me and says he can’t tell when he’s doing it and says he feels he’s just making conversation.
…But last week we woke up at my house he was on his phone and I saw some messaged with “😊😊” emojis on it. I asked him what he was doing and he locked his phone and said checking the time. I asked to see the messages but I think he opened a different chat and the chat was just his friend with a different emoji. Well this week he cleaned and organized his whole room and bathroom,he also moved my stuff around in the bathroom to one shelf. He also baby smooth shaved his ..area, And trimmed up his mustache, and asked me to shave his back. Idk, it all gives me anxiety, it’s a lot of change. I don’t have any real solid proof it seems. How can I get that proof…..i know a lot of people say “if you think he’s cheating break up”. However I have anxiety in relationships anyway, and I believe people with anxiety should still be allowed to date. Sometimes it just takes the right partner to understand the struggles that come with it.