<human>: Could you distill the essence of the text into 1-3 sentences?

My girlfriend and I have been "together" for about seven months.  By together I mean, agreeing that neither one of us would see anyone else.  We didn't really consider us in a relationship until about two months ago.
During the relationship I've come across a couple of red flags that concern me: 

First: In the middle of the relationship we hit a rough patch.  We fought a lot and she ended up breaking up with me.  We spent one day apart and got back together the next day.  During this day apart she hooked up with another dude, which I only found out because I pried.  Although we weren't technically together, it did bother me that she moved on to hook up with another dude the same day she ended it.  

Second: She frequently texts her ex-boyfriend. By frequently I would say every other day.  They dated for five years and of course this bothered me tremendously.  Every time I would confront her about it she would make it seem like I was crazy and I was suffocating her by not allowing her to be friends with him.  Curiosity got the best of me and one day I looked through her phone (wrong, I know) and read a message to her friend.  She said that they had been flirting, and he was taking his time to come back to her.  I brought this up and understandably she was pissed at me for going through her phone.  I argued that the ends justified the means, which I still stand by.  She said she wasn't waiting for him to come back and it was a joke between friends.  I tried to put it behind us and move on cause i really liked her.

Ever since this she says I can look through her phone, which I don't really want to do because I feel like I don't want to further invade her privacy and trust.  However, I notice that she is still very secretive with it and deletes all her messages, which doesn't help with my trust issues.  

Am I crazy or is this behavior worrisome ?
<bot>: Dating girl for about half a year.  Red flags have come up in relationship that affect my trust.  Don't know if I'm being insecure or genuinely have something to worry about.