I've always had problems with heights, to a greater or lesser degree. I used to not even be able to climb ladders, and I still tend to have difficulties on cliffs and similar. As for scaffolding or anything like that, forget it!
I'm usually OK when flying, but it manifests for me if I'm flying low and then the ground suddenly falls away. The first time it happened was flying over the South Wales valleys in a helicopter, when I was at about 500 ft, and the next moment at 2500 ft. And yes, I think a sudden climb might have bothered me in the past, but I'm gradually getting used to everything, and there's not a lot in aviation that worries me now.
There have been threads on PPRuNe about this in the past, and I was amazed at just how many pilots were scared of heights. It was quite common. So don't worry about telling your instructor. He won't tell you flying isn't for you, or if he does, get another instructor! What I'd do if one of my students had this problem is find out exactly when and where they were bothered, and take things gently, eg by climbing slowly and gradually in your case, and making sure you were happy, so that you could get used to it...and you WILL get used to it!
At the moment it sounds like you're adding to your anxiety by trying to hide the problem. Don't! We all have difficulties learning to fly, and if this is the worst problem you have, you're very lucky.
Take care, and feel free to pm me if it'll help.
Whirly