When a couple is intimately involved and there becomes suspicion in the relationship do you feel it is wrong?

to go through measures of your lovers cell or the inbox or sent box of your lovers email.I have been dating this lady for almost 6 months she often tells me she wants to be my wife. She even looked at wedding dresses and started to making wedding plans and even made wedding invitations. Some of the big problems are she flirts on line and text diffrent guys that she just ment. One guy she told she was still single and another she told she misses him and wish she could see him. I admit I went into her phone and computer to find out my excuse I told her I dont want to catch anything and my second moth of dating her an ex came to her house late at night she swares nothing happened. I found that out from a friend of her. Well we hardly talk and it bothers me what should I do