I ended up doing counseling for a number of years also due to having anxiety/depression. I was on SSRI's for less than a year for depression (did not want to be on them long-term). The counseling was very helpful in making me talk through my anxieties and poking holes in them.
Make sure you have a good counselor that you're able to work effectively with.
You could talk to your doctor about doing the counseling without SSRI's and then adding the SSRI's if you're still having issues with your anxiety after a certain period of time.