Firstly, good for you for taking the initiative in getting treatment for your condition.
Recognising that you need help is the first step, then going out to get it is next, so you are well on the way to getting what you need.
If you prefer to try talk therapies to medications, there is nothing wrong with that. Give it a try and see if it helps you. For some people, that can be enough.
If it's not enough though, don't be afraid of medications - they can really help. The best evidence in the medical literature is that for anxiety and depression, medications + cognitive behavioural therapy give the best results for the most people. I understand your reservations about becoming "dependent" on medications - it can look like that and people might describe their "dependency" on meds to stay well. But it's not like an addiction where you develop a physiological dependence and have withdrawal if it is taken away. The medications are correcting an imbalance in brain chemicals (neurotransmitters). For some, to keep the balance corrected, they need to keep taking the thing that fixes the problem. It's a bit like saying you've developed a dependency on calcium in your diet, because if you don't have any your bones start breaking. Of course! You need it to stay healthy. If your neurotransmitters are out of whack it's just the same.
You might wonder why antidepressants are being prescribed when you don't feel depressed. Some antidepressants also have a good response against anxiety (i.e. they are also anxiolytics). Many meds that you could take just for anxiety tend to make you drowsy and affect your alertness and performance, so an antidepressant that also treats anxiety could be the better choice for you. Your doctor is trained to choose the meds that best meet your condition's needs, but if you have any doubts why not go and see another GP with an interest in mental health for a second opinion? It will still be covered by Medicare and might give you some peace of mind about your treatment plan.
You could also make a deal with yourself to try the meds for a fixed period - say three months (they do take a while to start working, so you have to be patient!). After that you can reassess and decide for yourself whether you feel better or not; if you don't think it's worth it you can stop taking them (but work with your doctor on this, you shouldn't stop suddenly) and try other options.
At the end of the day it's your health and you are in control!
