Yes, unfortunately both the deep dive and buoyancy are both mandatory to gain my open Advanced water cert. (I got to choose the other 3 specialties myself)
I've dived to 20 metres before with no problems. I didn't even realise I was that far down until I checked my computer. Yesterday I dove to 18 during my naturalist course with no issues.
My instructors know me well and know I'm a nervous person - I usually do one stupid thing a dive ie. descending without my regulator in my mouth or putting my wetsuit on backwards. I think it's due to nerves and not (until recently) diving regularly. I am getting better as I'm doing a dive approx once per week now I live literally next to the water and the boat is moored at my front door.