I just started learning how to swim in Jan or Feb, did a sprint tri (500 m) in July (was ready by June).
While I was ok being in the water from the neck down, (you could plop me in a lake and I wouldn't drown), I never got the hang of putting my face in the water without holding my nose, despite seemingly endless swim lessons as a kid. I always got water up my nose and/or swallowed a bunch, so I still have some anxiety about putting my face in the water (w/o holding nose).
I started out just putting my face in the water and gently breathing out my nose to balance pressure. Next I had to learn to swim freestyle. DH and I taught ourselves the Total Immersion technique through the book and DVD. The method starts you on drills, so I just did drills for months. The drills were designed to imprint the movements in your muscle memory, and this technique worked well for me. The drills progressed in baby steps, so it was a long time before I was doing anything that resembled a freestyle stroke.
I would practice 2 - 3 times a week for 30 - 45 minutes, and I always started by just putting my face in the water. If I didn't get in the pool for a week or more, I was definitely more anxious than when I went regularly. So long story short, I'm still not really comfortable in the water, I have to ease myself into it, but after a few minutes I'm fine. I'm hoping to tackle open water next season.
I think that's great you are taking lessons to avoid learning bad habits. Just give it some time. I know it can be frustrating if you're used to picking things up quickly, but patience and practice will ultimately make you a better swimmer.
The best part about going up hills is riding back down!