I can't add much to what Onix said. I am also another counselor in training who has had bouts with insomnia. I have never been a good sleeper, didn't nap as a kid and generally never been someone who sleeps the recommended 8 hours. If I get 7, it's a lot. Waking up at 5 has been routine for me for years.
The waking up in the middle of the night as you describe is definitely related to anxiety. But, it becomes a vicious cycle because you start worrying about not sleeping, which increases whatever anxiety was there.
What helped me was acupuncture, yoga, and decreasing my coffee intake for awhile (I have since resumed my one vile habit). For a couple of months I took a medication that was not for sleep per se, but it had the added side effect of helping me sleep, as I took it at night so the "sleepiness" would not affect my daily activities. However, my normal sleep had pretty much returned at this point. One thing I found that during this time, if I did really hard endurance exercise, it made the problem worse. But, moderate exercise, like walking, slower cycling, and hiking helped.
I am not against medication, either. Sleep medications can be used for a short time as others have said. And +1 on finding a good counselor. It might take more than one try.