Hi and welcome to the forum.
We need some more information before we can even begin to guess at what might be going on with your daughter.
First, how old is she?
How long has she been on the antianxiety meds?
What is the name and dosage of the med she's on?
Is there a specific type of anxiety whe was diagnosed with, as there are several?
These answers would help us, but for now I will give you a couple of my best guesses as to what may be happening.
If your daughter has just recently begun treatment with an antianxiety med, the weakness and lethargy could be minor side effects that should go away in a fairly short time. They are very common and nothing to worry about unless they get worse or do not begin to diminish with time. You say they keep her calm, but perhaps "too calm." It is possible, and I repeat possible, that she may be on a too high dose for her.
Antianxiety and antidepressant medications do not come in a "one size fits all" pill. We sometimes need to have our dosages upped or lowered or even changed to another med before we hit on the one that works best for us.
Since this is an obvious concern to you, I would definitely have another consult with the proscribing doctor and discuss these symptoms with him/her. I would, at the same time, talk about getting your daughter into some therapy. She is having anxiety for a reason, and while the medication will help her deal with the symptoms, it will NOT help her deal with the root CAUSE of the anxiety. If your desire is for your daughter to recover, then simply masking the syptoms will not help. My humble recommendation is for a combination of both the medication, which will help her NOW, and talk therapy to help her for the long haul.
Peace
Greenlydia