Firstly, long distance relationships can be extremely difficult to manage at the best of times. But nearly impossible when you’ve got trust issues.
Also this whole thing happened so fast (only a few days???). And if this girl is already saying she loves you after such a short time, chances are she's got some issues. Maybe, as you say, she likes the idea of you being there to talk to and as a kinda back up.
If you can't build up enough trust in the relationship to deal with the distance then looks like it probably won't work out. But what you need to figure out is whether you're willing to work out these trust issues you're having. From what you say it sounds like the distance is just too much. I'd recommend not starting a relationship with her if you're already having problems before you even start and you can foresee that distance becoming an issue.
Trust me, I've had a long distance relationship before and it can be really really tough and can really mess with your head. If you're already having these kinds of doubts/ problems, maybe its best to break it off now before you become too attached, because it will hurt less now than later.
"Every once in a while, declare peace. It confuses the hell out of your enemies."
-Rule of Acquisition 76.