Dear Jack,

I am glad you had a nice time together, and she even showed some affection in public. Seems very normal and natural how she behaved.

As for her jealousy, her reaction isn’t too surprising, specially if her flat mate was flirting with you. When she asked you “She’s quite close to you isn’t she?”, she was looking for reassurance that you’re not attracted to that girl and are committed to her. So try to give her that reassurance, and also not flirt back with her flat mate.

A healthy dose of jealousy is normal. It’s only when it becomes obsessive, if e.g. she would accuse you for no reason, or try to control you so that you can hardly speak to a woman without her getting jealous – that would be problematic.