Many paths in engineering will give you a rock-solid math foundation without condemning yourself to it for life. Math is an important way to develop the rigorous mindset you need to be an engineer, but it does not necessarily become your everyday tool; computer science is a great example of that (even though some aspects of computer science deal with specific problems like computability, computational complexity, or cryptography using discrete math). Other engineering majors (like aerospace engineering) use math as a tool to describe natural phenomena (physics). It is almost never math for the sake of math. The closest “pure math” engineering major I can think of is operations research (essentially process optimization); perhaps information theory within electrical engineering. These are relatively narrow forays. Even then, they are often heavily mixed with computational science and machine learning these days. But none of that matters: once you’re in college you’ll be deciding your path; it is nothing like high school.
You’re pondering dramatically different career decisions based on completely the wrong parameters (not your fault). If you want to know if engineering is for you, the question to ask yourself is: Do I like to use my ingenuity to create stuff that will be used to solve real-life problems? Engineers make, whether it’s a software product, a space ship, or an artificial joint. They make stuff that blows your mind and help improve other people’s lives. It is intellect and creativity at the service of humanity.