Hola Sarah 

We often use the verb contar instead of decir when what is being told has some details, like a little story or anecdote. In this case you could say "me está diciendo" as well, but the use of "contar" conveys that the person was not only saying something but "telling" with more detail -so everything that comes after is taken as "a few details about something" which clicks nicely with "contar". 

Here's a Kwiziq lesson on decir and contar where you have examples with both verbs and learn about the different scenarios where you'd tend to use one or the other. 

I hope it helps.

Saludos