I want to snoop through my partner's phone, is that okay?
I guess not! Would you think it was okay if he did it to you? Why would you snoop in his phone?
To see if he's cheating on me with my coworker.
You should confront your partner about your concerns, not snoop around. What you are doing is creepy and possessive.
I'm hurt, I think he's cheating on me. I didn't want to do this.
You can't be snooping anywhere. That is sneaky, try talking to him first and if you think he is lying still then you can give him an ultimatum.