Warm welcome to the forum, its so kind that you have taken the time to connect with us on behalf of your friend - she is lucky to have you <3
I connect with this post as I too found myself in a similar situation with a friend experiencing anxiety a couple years ago so can offer you some advice I have through hindsight.
Firstly, I highly doubt that you have handled the situation poorly, as opening up about a mental health concern is extremely hard and temperamental. It's common for people with anxiety to open up one minute and shut down the next, regardless of the way we react. It has more to do with how they are feeling than how we respond if that makes sense. In my case, I became worried and frustrated with my friend in that she would open up one minute and shut down the next. After she told me she felt horrible about this and me simple asking her was enough but that she just wasent ready to talk or acknowledge the problem. So know it's likely not you handling things poorly. to answer your questions:
What can I do to let her know I'm there to talk?
You can keep checking-in. If she is comfortable address it directly ask How's your anxiety today/this morning? If she isn't, try simple check-ins like How are you feeling? Keep that line of communication open for when she is ready. Try not to be disheartened if she doesn't respond, its the opportunities that counts. Pick times when you know she will be comfortable to talk like when you are alone, or walks etc.
What are some things I should and shouldn't do?
Each person is different, so when talking to her really listen and mirror the language she uses (some people say stressed or overwhelmed instead of anxiety).
I would avoid offering advice or "solving" at this point and explore, try:
- How would you describe it?
- What are some things that help when you are feeling X?
- What are things that don't help when you feeling X?
Whats helpful to hear?
If you aren't already encourage her to do the things she likes to do for herself ie. self care activities and join in. Even say you want to do them to get her to come alone! Going for walks, cooking, arts and crafts, whatever it is, it's a good opportunity to have fun and destress. It also models appropriate ways of coping and allows more opportunities to talk.
Less can be more, so listening is a good start. Remind her that this does not define her, that you still see all the wonderful things she is, and that wont change <3
Keep us updated!