My handwriting is awful. I can not physically correct it, do I have a real problem?

I have very poor penmanship and its gotten worse, not better since high school. I'm a full time college student so it hasnt mattered much for my school work except for when people ask me to copy notes. When I have to hand write homework its very messy and most of my TA's or professors have to work really hard to understand. When I try to write neatly, I literally can not unless I write very slowly, and even then it looks like a 7 year old wrote it. I've been playing piano for years and I think maybe this is related to the early stages of carpal tunnel? I'm left-handed by the way, but I don't think that really matters. I should also add that I draw very well and I have never felt as though I should be right handed instead. Believe me I've tried and it feels all wrong. Thank you for your answers!!