I had the same concerns once my and my now fiancee started getting serious. We had a few arguments about facebook messages and things as well, but I was going through a divorce at the time and didnt want to get anyone any more emotional than they needed to be.
Ive had plenty of lectures from friends and doubters, almost all well meaning, and I understand and actually appreciate that, because all anyone hears about LDRs is the scamming and the problems.
Unless you start looking around, you don't hear the good stories, and even when you DO look around, you still hear these stories and I have to admit Ive had a few bad moments when my insecurities have got me worrying about stupid stuff.

Ive now accepted the fact that everyone thinks I'm nuts. Ive come to the conclusion that actually, they're right. I AM crazy, but I dont care. I'm just crazy about my future wife.