Christ, don't think of weekly or even fortnightly visits to her.
She’s finding her feet, finding friends, and her mother being around like that is very much not what’s required in the first term.
I imagine your neediness would be apparent to her and could even be absorbed as some weird kind of guilt. Whatever about that, I think you just have to bite the bullet and tell yourself her new life is the important focus here, and let her get on with it.
If she misses home, she can communicate that to you, but don't insert yourself into things at this very important point in her uni time.
First term is daunting, often scarily so, but it’s a very important transition for a young person, and I think parents are best at the other end of a letter (email)/ call than there in person, so as not to cause confused signals in a brain which is still in some ways a child’s but at the same time, an adult’s, with a challenge (i.e. becoming self-reliant) to handle that is just as important as attending seminars.
Do try to find another outlet for your emotional upset; you’d be doing a great kindness to your daughter. Concentrate on the Christmas break!
The time til then will fly by, and of course, you can FaceTime with her maybe once a week (until that happy day when she excuses herself as she has a gig/ party/ sit-in to attend!)
She’ll be grand, and so will you, OP. Hang in there!