I published a story that had lots of online chats/emails/texts between the main characters. I wasn't sure how to write it when I was starting out, but my publisher and editor helped me figure it out. Here is an excerpt from the published book and what we came up with. I hope it helps.
The rest of the trolls in the chatroom faded away. Percy
didn’t even notice their words or silly emoticons, all he saw was
MaxTheMagnificent. After polite conversation for a few minutes,
Max pinged Percy into a private chat.
He was suddenly nervous. Laughing at himself, he
couldn’t understand why Max had this instant effect on him.
Maybe it was the fact they were actually talking. All of Percy’s
previous encounters with men had been purely physical…with
Max, it was different.
Max: Binx? Hey? Are you still there?
Snapping back to reality, Percy noticed he was
daydreaming about Max while chatting online with him.
Binx: Sorry, I’m still here.
Max: Where did you go?
Binx: Nowhere, I got lost in my thoughts for a
moment.
Max: What were you thinking about? If it’s juicy you
better dish!