Are you on any medications for your anxiety/panic & depression? If so, is it just recently that you began taking them?
The feeling of being off balance or even of the floor moving under your feet is fairly common with anxiety and panic attacks. The weakness in your legs I'm not sure about. It COULD be related to some meds, but without knowing which, if any, meds you're taking, I can't even hazard a guess, and not being a doctor, I don't think "guesses" on my part would ease your mind much anyway.
The off balance feeling MIGHT be an inner ear infection which can cause that symptom, but I think the smartest thing you can do is get to your doctor and talk to him/her about all of this.
Let us know how you're doing, OK?
Peace
Greenlydia