Well, possessiveness is bad (for lack of a better term) because you don't own him. You can only possess something you own, not a person.

That being said, I understand feeling that way, I feel it sometimes, too.

It's very hard to not even have the foundation and security of a long-time relationship to go on when adjusting to this.

What are you scared of? Don't be shy. Of him falling in love with someone else and leaving you? Of him being with someone you think might be prettier, smarter, wittier? Of being home alone while he's on a date? What scares you, put it in your face, and then talk to him about it.