He wouldn't be begging to arrange a meeting with another woman if he were exclusive with you. This guy apparently lied to his other girlfriend, lied to you, and then lied again when you caught him trying to double-time.

If he hadn't lied about what he said to her, it might be possible to buy his story, but you read his texts and caught him in the act.

Better to find out now rather than later, I guess. I'm sorry