Dina, yes you can do this. I know what you mean about the tiny strips. My mom and I took a class on how to make on years ago. She sewed the strips all the same way and they shifted on her; I tried to tell her last strip out - first in. So hers were going downhill; she couldn't get it together so I brought it home with me; I had to take out many, many of those small pieces and correct the seam allowances before they would 'fit'. Like others have said; when it gets frustrating, take a break or give it a day. You are making great progress and it's going to be fantastic when you get it done. Just keep plugging along.
I also have that pattern and many others I inherited from my mom's stash. I should get busy on another one. I enjoyed it; it's not a wasted day if you learn something new!
Don't give up. You CAN do this; be sure to post your final project.