Your little angel could just be reacting to YOUR anxiety. If I am reading this correctly, she is your first child, so this is probably as new to you as it is to her.
She reacted this way in the beginning for whatever reason (soap in the eyes, ears, or just fear) and that reason may have been long ago resolved, but because she has done this so often, you now EXPECT her to do it, and when you are ready to wash her hair you unconsciously tense up. Kids are experts at picking up on and reflecting adult tension. I suspect this because you said she did great for your sister.
If washing her hair in the sink is working for you, then you need to do what is comfortable for you both for now.
In the meantime, start working on making shampooing less stress for both of you. When she is in the bath, work up a little shampoo lather, put it in her hands, allow her to pat her head with it, squish it, play with the bubbles in her hair, just have a fun time, all the while CALMLY talking and smiling. You might even provide a hand mirror for her to look at her self with the "pretty bubbles" in her hair. If you do this at the end of her bath, then you can always remove her from the tub to rinse her hair in the sink, where you both feel comfortable. That will be a little extra work at first, but I really don't think this phase will last much longer. Especially as you begin to gain confidence in yourself.
Something to keep in mind to help yourself calm down ..... if you have done all you can to be sure she is not hurting any where, then even though she is screaming, there is NOTHING WRONG with her. She is just voicing her opinion. Don't let her shake you up. She is going to voice her opinion loudly on a LOT of things as she grows up.
The biggest reason a crying child upsets us as parents is because we believe something MUST be wrong if she is screaming that loudly. That is not necessarily true. When we are sure that there is nothing wrong, it is amazing how easily we can ignore a loud opinion, knowing that she IS fine, and she WILL be fine. When you get a good grip on that concept, you will relax, she in turn will then relax, shampooing will no longer be a big deal, and you can pat yourself on the back for learning a valuable parenting skill early on that will come into use countless times even well into your child's teen years and early adulthood.
Take it from someone who has been down the road of new mom, experienced mom, new grandma, and experienced grandma.
Just the fact that you care enough to want to make this a pleasant experience for you both, tells me you are a loving, compassionate, interactive Mom who wants to do the best she can for her child. Your a great Mom !