Try not to act jealous, because if they believe you are jealous they may keep it up just to spite you. Instead, let it roll off like you don't care. Sometimes just relaxing and being less possessive helps the other person feel less trapped and less like a hotshot.
No doubt she has feelings for him and shows it without any reserves for propriety, perhaps aiming to snap him up if and when you two ever split. Try not to let it get you down. Take care that you remember your own self-maintenance: nice clothes, hair, and makeup help people think you feel good about yourself. When you respect yourself they are more inclined to respect you as well.