When your girlfriend says don't like pictures of other girls, do not do it. When she tells you not to entertain messages from other people, you better not do it. It is not being immature or being possessive but you are giving her reasons not to trust you. You are only giving her a hard time. It is not being dramatic but girls get jealous easily. For you it might be just small things but for her at some point it makes her question your loyalty.