Summary: Ask questions to learn her beliefs. Then reason from within her beliefs.
I have tried bringing it up gently, asking how things are feeling and trying to politely point out evidence that I see of the medication affecting her.
Sometimes I try to convince people of things. Sometimes I start with some reasoning (A therefore B). That's rarely effective. Instead, here's what I find effective: starting from what they already believe. To find out what they believe, I ask questions.
In your case ask: Do you think your medication has made things worse? Yes -> Do you think it would be a good idea to change your medication? No -> rather than state the evidence ask questions that confirm the evidence. Learn what evidence she sees. Then assimilate that into what you know. Then proceed from there.
Why ask questions? I've never thought about this before, but by asking questions, you're putting her in a learning mindset. She's literally questioning things. So she's more likely to be receptive to new ideas. But if you give statements she may have a tendency to get defensive or argue against it, thus not being receptive to new ideas.
And of course asking questions means you understand her better, so you're more likely to give a compelling argument.
Other questions that are good to ask:
What do you want (in terms of your anxiety)?
For example, she may say she wants her anxiety to go away. Then you can ask, well has it satisfactorily gone away? If not, does it make sense to talk to a doctor to figure out what to change to make things better?
An advantage to this is rather than stressing how things are worse (which she may or may not agree with), this stresses making things better, which is arguably always possible - so she may be on board with that, even if you disagree that the medication is making things better.
Another question to ask:
Are you perfectly happy with your anxiety symptoms? If not, would it be worth it change something so that you can be happier?
but refuses to tell them about the panic attacks
[Watch I'll do it to you :)] Do you know why she refuses? If not have you considered finding out why? Make sure you understand before you suggest anything.
claims that the new medication is helping her
Same thing - do you know why she's saying this? Does she really believe it?
My answer is based on experience. I've spent years feeling misunderstood. All I've found I can do is change myself. I've found many approaches that increase the liklihood that someone understands me. This is one of them.