The contact under a name thing is such an old trick. The deleted messages isn't as much of a red flag in my opinion, because I don't keep all my old messages either, but it's shady af to put someone else's name under a contact in your phone. At the same time, it could mean nothing. You have to talk to her about this and find out more information before jumping to conclusions. You need to talk to your girlfriend about how you feel and about the issues in your sex life, otherwise it will never get better. Maybe she feels unattractive, or maybe you don't do enough to make her feel sexy when you want to get down and she feels awkward. Maybe she's simply not in the mood. Having children with your boyfriend who works out of town would be very stressful, I imagine, and she may have a difficult time getting turned on.
Again, you need to talk to her about this and see where she's coming from.
"Caring is not an advantage."