"Jenny" is sweet, but over paranoid

Dear John Q,
I am a 27 year old man who, for the past three months, has been in a long distance relationship with a 44 year old woman from Canada. We text and chat regularly on the phone and through instant messenger. Some of our conversations have gotten a little sexual. “Jenny” is a very sweet woman with a heart of gold, but lately I feel she has been getting a little over paranoid about how I communicate with other women on the internet and in real life. I admit that while we have been in a relationship, I have been known to flirt with other women a lot, especially with a supposed 24 year old nursing student named “Laura Johnson” whom I once had communication with on the Internet, who was really the work of a Nigerian scammer. One night, Jenny went undercover in the chat room where we normally hang out and caught me flirting with other women, as well as her fictitious screen name and persona. She confronted me about it on instant messenger, feeling very sad that I could break her heart like that. We talked to each other on the phone for about two hours and I did my best to comfort her and tell her how much I cared for her deeply and that I didn’t want to lose her. She eventually forgave me, giving me an ultimatum that if I did it to her again, it will be the end of our relationship. Lately, she’s been hearing rumors that I have continued to flirt even more with women in our chat room and on Facebook, which I swear is not true. I am much more committed to my relationship with Jenny now and am finished with my player days. I don’t want to lose my friendship or trust in Jenny, yet I don’t want her to lose those things with me either. Is this woman the right person with whom to have a relationship? -California Cub