She thinks I'm flirting with other girls, how do I tell her I'm not?

[CM]

This girl I've been semi-dating has been giving me the silent treatment because she thinks I'm flirting with another girl on FB in the comments on a status I posted, and won't answer my calls and texts, so idk how to talk to her.

Her: I wuv this and you! Miss you
Me: Love and miss you too! You're the best! lmk if you eventually manage to save every german shepherd on the planet, I'll throw you a party!
Her: omgoodness you just made my day! I'm gonna I swear! <3
Me: An adjective does not exist to express how awesome you are
Her: You're too sweet <3

The thing is, I'm friends with her boyfriend, I have a picture of the three of us together on my phone, he sees everything we write on FB and trusts me, because I'm like this with everyone, and that's just how the two of us talk, because we're both the type of people who like to make ppl happy, and random compliments, but this girl I've been talking to doesn't know this, and idk what to do.
Babette - the girl I'm seeing doesn't have a boyfriend, the girl she thinks I'm flirting with on FB has a boyfriend, but I'm friends with both of them, he sees everything we write, and knows that's how I am with everyone, but she thinks I'm flirting with other women.