It is common for mental illness to first show up in the late teens and early twenties. Just be aware that your daughter anxiety could actually be the start of an anxiety disorder. This happens to us and we never saw it coming. After the fact yes but not before. Just keep a eye on her and keep the dialog going.
I also recommend that she go to the counseling center as early as possible. It can be VERY difficult for a student to ask for help. They often don’t want to admit they need help or have what they see as a weakness, Hopefully once she see the numbers of kids that are waiting for appointments she will understand that she is not alone. It is scary how many student at my daughter’s school are suffering from these issues. And that is just the ones who have taken the first step.
It is also possible that once she gets settle in that all will go well.
Not really an anxiety pill, but my anxiety-ridden child has had success with St. John’s Wart when we knew she would be away from home for awhile. (She went to sleepaway camp for weeks at a time starting at a young age; the anxiety showed up around age 11.) However, SJW doesn’t really start taking effect for several weeks, so she would start taking it about 2 months before. Also, we have found that Zzzquil helps with sleep during anxious episodes - anxiety gets worse when your kid is lying awake at 3 am.
With college counseling services, demand can frequently outstrip supply. I’d look into it thoroughly and second (fourth?) the suggestion of researching local counselors outside of school. The other thing is it is best to find a therapist who meshes well with your child. Often, on a college campus you get who they have and it might not be a good fit for your daughter. Finding a good fit seems very important from those I have talked to who utilize psychologists/therapists.
If you think your student may need counseling, there are a lot of questions you can ask on a college visit:
Go find the counseling center - how far away from dorms and classes and such? Is it a pleasant place to be or a dump?
How long is the wait list to see a counselor? A week? A month? Longer?
How many visits are allowed per term?
What else is available for kids who are denied access to counseling or have used up their visits? For example, is there a mental health alliance club, etc.