Jealous girl making up stories in her mind?

the girl ive been having with is very jealous, she makes up stories in her mind that im talking with other girls, she looks at my phone (tries to sneak a peak when im texting) and I dont appreciate it, she has admitted to me that shes a very jealous girl at times, I guess I have to decide if I can live with that. Some days everything is good, and then other days she fabricates stories in her mind. We are in a committed relationship and it was just made official a week ago, she was ecstatic when I decide to make it official, however most of the time we spend together is spent with her being upset about things that just arent even happening then we have and everything is fine untilthe next time she makes up another story which is usually the next day, I know I deserve better, do you think this is just a phase because the relationship is new or do you think she is going to be this way