You remind me of myself.

I think this (being there without being clingy) is something you learn to gauge: being present, recognizing how you feel, paying attention to the other person’s reactions, and adjusting.  This is difficult to do when you’re feeling anxious, but you can do it to whatever extent you feel able in the moment and that’s good enough.  This balance is not like walking a tightrope, where if you mess up you fall to your death.  It’s more like driving: you pay attention and stay in the present moment and if you get off track you adjust, keeping yourself on the road.  Sooner or later you will notice and adjust.

I agree with Anita, long distance is difficult!  Do you have plans to live closer to each other?  I think that is the best setting to learn that balance between together time and alone time.