I can't tell you about the mechanical engineering major part because I majored in Computer Science, but I can tell you about the algebra vs. geometry thing from my personal experience. I loved geometry in school, always scored full marks in it. I loved to figure out how to solve the problems based on the theorems. But algebra never made any sense to me, exactly like it doesn't to you. At that time, everyone told me that I need to work hard and practice algebra, but I never understood that kind of a virtual x and y stuff. Also, I invariably made silly mistakes and messed up the problems and scored poorly there.
Later I read that there are some people who love geometry and are bad at algebra and vice versa. (http://teacherscount.wordpress.com/2009/12/21/which-did-you-prefer-algebra-or-geometry/)
For you, as you love robotics you are anyway far ahead of many future engineers. Don't let algebra dampen your interests. All through your life there will be some subjects that you don't like. Treat algebra as one of them and try your best to score the best according to your potential. Maybe ask a friend who is good at algebra what she does to solve the problems, or just practice a little more. Math practice is always good in the long run.
You can definitely choose a medical major if you like it, but don't do that just because you hate algebra. Maybe some mechanical engineer can help you in knowing exactly how much value algebra has in mechanical engineering major.