Congratulations! Engineering could use people with proven skills that want to succeed.
If you have desire to always understand how things work, you've already got the first requirement. A story - remember a few years ago when you first started seeing the imposed yellow line on the field of televised football games to indicate the first down line? 99% of the viewers saw it, liked it, thought it was neat, and that's it. Well, being an engineer, and understanding that those very simple little lines required ENORMOUS amounts of technology to appear correctly from all angles, and all zoom factors, and all field conditions, and all weather, every time, I verbalized my curiosity on several occasions. In fact, it got to be a "thing" with my entire extended family. Whenever I was in the room and a football game was on, someone would always say. "How do they make that yellow line?" And everybody would laugh at the weird engineer who spent more time trying to figure that out than watching the game. The other members of this forum will agree - you get used to it.
A good way for you to start would be to take some drafting classes. Notice - I didn't say COMPUTER drafting. I said drafting, as in a pencil, paper, and a straightedge. Manipulating those tools to create drawings like you see in the books causes you to STUDY those sample drawings very carefully. It also gives you an appreciation for what it takes to produce a good, attractive, usable drawing. I'm not sure where you can even find manual drafting classes anymore, but if you can, take some. Then, after breathing eraser dust for a while, move into computer drafting, CAD.
One thing you will learn in that process is which branches of engineering seem to hold more interest for you. For example, you mentioned mechanical and systems. Believe it or not, even those two fields are HIGHLY diverse. For example, a mechanical engineer could end up designing buildings, or bridges, or HVAC systems, or piping, or aircraft, or automatic machines, or consumer products, or entire manufacturing plants, or power plants, or production equipment, ... Each one of those specialties will require a different body of knowledge, but all could start with a mechanical engineering degree.
My work has always been around manufacturing of some sort. You might consider this: most companies that have an engineering department have both degreed and non-degreed personnel on staff. Very generally, the non-degreed individuals might be called "designers", while the degreed folks have the "engineer" title. The designers usually aren't expected to know how to do the detailed engineering calculations, but they understand the concepts very well. And they know what it takes to make things work. I ahve learned a lot from the designers I have worked with over the years. If you aren't sure about pursuing the engineering thing all out, you might make your goal to become a designer. Usually all that takes is a little technical schooling and some good drafting skills. That would give you a very good insight into the working world of the engineers around you.
I could go on, as most on this forum know, but I'll stop for now.
Except for this - don't worry too much about sketchy math skills. You will be amazed how much more sense that all makes, and how much easier it is, when you are applying it to real world applications you can understand. Plus this - I barely passed calculus in college and flunked differential equations altogether. That fact has had zero effect on my career.