I'm going to go against the grain here. I don't believe in emotional affairs. Either the person is physically cheating, or discussing cheating (affair) or they are not. I find the term emotional affair basically akin to blacklisting any close friendship with someone of the other sex.
I'd also say that it would be over my dead body that I'd hand my phone over to anyone to check my messages, if I CHOOSE to share something, that's fine, if I'm being asked to give up privacy to make someone else feel better, that's not.
There are plenty of things on my phone I wouldn't want anyone else seeing. For example my friends discussing private issues, my friend's privacy in the things we've been discussing, is worth more than your anxiety over what that discussion could be about, some of the conversations I have with friends are highly personal for them, about SA, or DV and if they have not explicitly consented to someone else knowing, then it's not going to happen.
There is also the other possibility that they are discussing you, they are discussing your behaviour and he's asking for advice. Not unreasonable to have a private discussion with a friend of whichever gender about a relationship you''re struggling with but that's just my opinion.
The best thing could be to be honest. "I'm feeling really anxious about my relationship with you, and am upset that you appear to be having long conversations with another woman and talking to her more than you're talking to me. Can we just discuss where we are, if we're in a good place, or if you're unhappy?"
If your other half is cheating, give them a calm opportunity to admit it, without flying off the handle before you even know if they are or not. If they're cheating it's up to you what you want to do about it, but a calm conversation is much more likely to get to the truth than getting angry and accusations.
I do hope that you find a way forward though.