Yes, nervousness is normal. Please stick with it. I did not.
I had about 15 hours as a student when I went on a solo three-leg cross country. I bounced my Cessna 150 on a couple of landings. No damage and things generally stayed under control. But that feeling of bouncing up while the plane is slowing, knowing you are getting closer to a stall really spooked me. I can feel it now. That was many years ago and I have not flown since.
Not to blame others, but I had an instructor who was a "cowboy" where I was more on the quiet side. It wasn't good chemistry, but I did not see it at the time. I should have immediately switched instructors and worked through my landing issues. You have a good relationship with your instructor, thank goodness. I am sure that as you develop competence, which I did not, your nervousness will lessen. As indicated above, its OK to keep a little apprehension of what's going on, to keep you safe.