I am am mom of a 19 year old...and let me tell you, the "missing them" and "worrying" never stops no matter how old they are. It's called being a mom. When my daughter was around 16, my husband and I allowed her to travel alone on a plane to New York for a week to stay with friends. This was the first time she had ever been away from home for more than a night and also the first time on a plane. I about went out of my mind. BUT, I kept busy. I mean busy, busy, busy :-)
I got through it and she had the time of her life and thanked us over and over for letting her go. Trust me, your daughter is missing you too, but there are times we need to let go (of course, there are times to say no too). But you get the picture. Good luck and hang in there. You're not alone in your feelings :-)
L. B