Hi, Colima, and welcome!
First of all, I'm sorry you're going through rough time, but you've come to a great place for support.
Your boyfriend's relationship with this woman does seem a bit fishy. If there's nothing going on between him and this girl 15 years younger than him, then why does he feel a need to lie to you about it? What's even fishier is that he tries to make it sound as though you're irrational for being suspicious of this in the first place. If he's 100% in this committed relationship with you, then he should have no problem being open and honest.
One question I have is, how do you know what exactly he said in the messages he texted to her? I can't say I condone going through someone's phone for answers, but if you feel a need to snoop in the first place, then that's a clear sign that something is wrong in the relationship that needs to be addressed. I agree with you that his behavior is completely inappropriate - generally, if you're content in a committed relationship, then you don't feel a need to flirt with other women. If he's going to try to play manipulative games with you and try to make it sound as though it's your own irrationality and "unreasonable jealousy" (i.e., YOUR fault) for suspecting something's going on, it comes across as though he's trying to hide something.
Bottom line: don't allow yourself to feel as though you're being irrational for noticing his overtly shady behavior. He's using a common technique that people use to dodge the subject at hand - it's manipulative and unfair. Don't let yourself be treated like that.