So, the message to your friend in your Messages application shows blue chat bubbles (iMessage) or green chat bubbles (SMS)? If blue, then yes -- somehow your friend is being detected as an iMessage user, but if green, the problem MAY lay elsewhere.
Your post suggests that you'd thought of this -- since you distinguish between iMessage and Text Message; but didn't specifically mention any colours, so I thought I'd ask. 🙂
Next, I'm assuming that your iMessages/Text Messages go out to everyone ELSE fine, just not to her. And that she receives everyone else's Text Messages, just not yours, right? And that you can receive hers? She may have accidentally blocked you? (I know that last leap depended on previous assumptions but thought I'd throw that out there ahead of time). On the Samsung messaging app, 'Delete' and 'Add to Spam' are right next to each other.
Good luck and keep us informed.
Edit: oh sorry, I see that you posted that none of your messages to her are being sent, as opposed to none of your messages to her are being received. Possibly your message thread between you and her has become corrupted. Is your phone low on storage? Do you have a lot of messages stored? If all else fails, back up and delete the message thread?