I was going to start this out by saying that some people saying DiffEq isn't "higher math" are math geeks and that they're over-emphasizing math... But then I went back and re-read the OP and, well, maybe they're still overstating the case, but they do have a point.
If you really want to go for a career in computer programming, you will need a more solid basis in math than a good understanding of long division. You need to be able to do function based math (grouped under Algebra when I learned it) in your sleep; you will never be any good with computer code if solving simple equations and reading functions isn't second nature to you, regardless of variable names or format. And all of those proofs you did in Geometry and then probably again in Calc I and II - that's formal logic, and if you can't apply formal logic at a whim, computer programming is going to be a rather rough life for you.
Beyond that, statistics and probability, linear algebra, matrix algebra, trig, vector math - these are things you're likely to run across sometime during your career. Maybe (probably) not every day, unless you're in a job that utilizes them heavily, but they're good to have learned at one point so you know where to start 10 years down the road when you run across that situation.
If you really got through the math between long division and DiffEq without really understanding it, I'd recommend going back and working through anything in the above list until you do understand it - and if you have more advanced math ahead of you, include Calculus in your review. If you need a tutor for it, get one; or audit lower level classes as refreshers; or find some book that explains things in terms you understand. Also, if you don't know it already, understand your own learning style and find something that matches your style; understanding how you learn best can help immensely as you go forward.
PS - DiffEq is a bit different; I had zero problems with math classes (aside from being bored) until I got to DiffEq. I did calculus, complex math, matrix algebra, prob&stats, and linear algebra all okay - don't know what it was about DiffEq that tripped me up. Don't feel bad that it seems difficult - it isn't simple. It's also nothing I have used in my career as a software developer.