It is never too late! I never took an engineering class until I decided to get a masters in it. I finished my bachelors degree in physics and decided that it was not a career path that suited me. Perhaps I felt the same way you do. I had never had an engineering class but what I did know about it had me interested.
If there is still an opportunity to gain some engineering experience through a internship or shadow program take advantage of it now. If not, put together a personal statement that highlights all your best qualities and don't worry so much about others have done. You might ask a science or engineering teacher or guidance councilor for help with technical language. It is important to let the university know that you have the desire, curiosity, and enthusiasm to learn engineering. From personal experience, mechanical and aeronautical engineering are challenging but infinitely rewarding fields of study.
And, if you find that they don't suite you after taking some courses, at least you'll know for sure.
Best of luck!