I strongly recommend jumping ahead as far as possible. You can pick up a used textbook or scope out the Khan academy
to brush up on anything you missed. The worst that’ll happen is you’ll realize a few weeks into the advanced course that you need to switch down a level, and do so. But if you don’t at least try to start at an advanced level, there’s a good chance you’ll always be a semester or more behind where you could have been, and your courses will be quite boring.
The rules of algebra are pretty intuitive once you understand that it’s just arithmetic with letters. Most of the time you’ll start off with two things equal to each other, and you want to do the same things to both sides so they stay equal while you rearrange terms. You definitely want to learn trigonometry and calculus for engineering.
They are also pretty straightforward at least conceptually. The trig functions sine, cosine, and tangent are just ratios of the side-lengths of right-angled triangles. As in, measure one side of the triangle, measure another side, and divide one value by the other. All the rest of it is just uses of the Pythagorean theorem and rules for similar triangles.
Calculus is at heart the study of limits, but from a practical standpoint it just tells you how to calculate rates of change (the derivative) and accumulated totals (the integral). There are a few basic things that get proved, like the derivatives of polynomials, trig functions, exponentials, and the chain rule, and the idea that the derivative “undoes” the integral (in the sense of being inverse operations). After that you almost never have to touch limits again, at least not for engineering.