Your reply brightened my day! I'm glad this made you feel better, because it's so familiar to me and it's overwhelming.
I'm glad that I'm learning these lessons and addressing them now so I can hopefully make our relationship healthier similar to what you say you have now.
Hell yea! Believe me, when you can drop your girlfriend off at her house, and instead of getting super upset, feel proud of how great you guys are together and how happy you are that she loves you and that you love her... that's the level headed joy worth aiming for. It's not always like that, there are ups and downs, but you'll know when you start getting there.
The personal mental security needed to get there is aided by setting up multiple avenues of personal meaning and self-love. In the abstract that's a huge crazy beast to conquer, but in practice it's really just making sure you have things in your life which give you fulfillment: setting work out goals, doing a good job on your studies or work, reading books, taking part in some form of community (be it specifically social or otherwise), whatever it may be. These things won't manage to give you as much fullness as good loving time with your girlfriend will--if bike riding could make you feel that complete wholeness you'd just date a bike-- but they'll keep you from fluctuating to such extreme states of fear and need so quickly. Once the mental road smooths out, the relationship will prosper.
I mean think about it, it sounds like you love her and you're really caring toward her, and the same on her end toward you. So realistically the biggest impeding force from making things feel OK is fear: if not dealt with it can turn into unintentionally guilting someone into things or whatever. Then the problem is worse than it ever needed to be. The fear will also keep you from dealing with problems in the relationship appropriately: if she ever does something which is hurtful, whatever it might be and however minor, you might be too caught up in this high-intensity thought pattern to be to calmly have the conversation where you say "This hurt my feelings" and she apologizes and you hug it out. Conversely, if she approaches you with a problem, you might just break down rather than dealing with it head on. If she knows you might, she will hesitate to bring problems up if they are minor, and then your communication suffers.
Definitely keep talking it out with her, and whoever else you can trust (on the internet or otherwise). Be careful about what you write on relationship advice message board though, like I said before, everyone's advice is biased.
Best of luck to you both! That good lovin' is something to cherish.