"I've been diagnosed with anxiety, and put on medication. I've been told it's an illness? Can I ever get over this?"
Anxiety is a universal human experience. It's our emotional alarm system and it exists to warn us of impending danger. It is a highly advanced, highly sensitive system, but unfortunately it is prone to malfunction.
Anxiety is not an illness or a disease in the conventional sense of the word. You aren't born with it and you can't catch it. It is caused by a complex combination of things, including the natural sensitivity of your alarm system, (largely your "amygdala" which is part of the limbic system in the brain) and the events of your life and childhood that you live through. It's heavily influenced by trauma and life circumstances.
And, although this might sound strange, it's not really the anxiety that is the main problem.
The natural, programmed behaviour when we feel fear and anxiety is to avoid. It's the old "fight flight" response. The problem with anxiety arises when it malfunctions. It causes us to be fearful of events that haven't happened yet, and in turn make decisions to avoid them. By avoiding them we never get to challenge or overcome the fear: in our mind whatever is frightening remains frightening, and the avoidance reinforces the fear.