Overcoming a profound basis of underperformance as a freshman Relevant background: 

Freshman at large public research university, pursuing Engineering/Applied Mathematics dual major.

Labeled 'gifted' after neuropsych evaluation in Elementary school. Processing speed about 2 standard deviations lower than other subscores, this may have contributed to learning maladaptations that have become evident in University.

K-8: Programs where I got A's and B's without actually making the effort to learn the material. Never a straight-A student, usually got discouraged when my (also 'gifted') peers did stuff more quickly than I could, decided I didn't like what I wasn't good at.

I got a few A's but mostly B's in high school math, where I completed up to Multivariable Calculus, in which I received a B. 

This semester I took Linear Algebra &amp; Differential Equations (1 course) which comprised 2 midterms and a final. I got an A on the LA midterm, didn't have much trouble with that. However I got a D on the DE midterm; it turns out I can't integrate worth a damn anymore. My final grade is TBD, but I'm guessing I will earn a B in the class. 

The cruel irony is that by the time I realized I enjoyed math I also handicapped myself to learning it.

Question:

Has anyone here been in or witnessed an applicable situation? It feels as if I've dug myself a hole that may not be possible to get out of regarding future math classes.
The cruel irony is that by the time I realised I enjoyed math I also handicapped myself to learning it.


I've had a somewhat similar experience so I'm going to describe it in a few words. Perhaps it will be helpful for you. 

When in school I was labelled "gifted" as well. I was a member of a club for children with math aptitude and participated in competitions but never put in any effort. Eventually, after entering university, I realised that research is what I really want to do. That is the most important thing, I believe. I would have been smarter if I studied seriously in school. Sometimes I regret not doing it. However, it's in the past, it doesn't really matter, it's not relevant to the present situation. You have a goal and your current skills as starting parameters. What happens next is up to you. From your background section I got the impression that you think about what you could've done a lot. My advice: think about what you can do instead. Right now you're in a perfect positions to study what you like! Some people face a lot more difficulties. 

Now to address your actual question.


  Frankly, I don't quite know where to start relearning. Where would a starting point be?


I don't think you actually need relearning. Judging by your grades, you have a pretty good grasp on the material. If you really need to sharpen your skills do some exercises from a textbook. What I think you should do (it worked for me) is pick up a book/ online course / seminar on the topic you are interested in and just start learning. Whenever you encounter something you don't remember from the classes go back and refresh this knowledge. Eventually things you really need from those courses will become second nature (and this way you can avoid deliberately solving boring exercises).

You edited the last part out but it did indeed sound like the impostor syndrome. There is a ton of people with imperfect knowledge in academia, both students and teachers. More importantly, you're only a freshman. Even if you don't get into that cool project next year there will be other opportunities. You have a lot more before you than behind you.