I think it’s okay not to take a diagnostic at the very beginning if you think it will be de-motivating. You know yourself best. I’d still try to take one at least sometime in the middle of your studies, as opposed to just at the very end. That way, you have enough under your belt to hopefully not get a scary demotivating score, but you have an idea where you stand and what you still need to work on while you still have time to work on it.
Actually, I think there’s a chance the “super basic algebra” you do in your major will be more of a benefit than you might think. E.g. do you still remember how to factor quadratics? Rules for exponents? Basic rules for orders of operations? Yes, there will still be lots you’ve forgotten, and even a little bit you may never have come across. But you won’t be starting from scratch. And you probably already have a decent intuition for numbers.
The GMAT has two types of problems - data sufficiency, and problem solving. The data sufficiency is unique to the GMAT, so you should try to practice some of those during whatever limited studying you do during the semester so you’re used to them. The problem solving ones are similar to the SATs (don’t know about ACT), but with slightly harder math and a slightly different emphasis. They don’t allow a calculator, so some of the test involves intuition with estimation, patterns with numbers, etc. So you may want to start re-memorizing the decimal equivalent of common fractions, tricks for doing multiplication and division easily without a calculator, etc.
There’s also some math you may not have come across before if you haven’t taken statistics. But if you’ve taken business statistics or something like that, that would cover most of it. It’s very basic stuff like mean median mode, standard deviation. A bit of probability (which might not be covered in business statistics?) - combinations permutations etc. If that all sounds unfamiliar to you, that might be a good place to start teaching yourself now during the semester. You could pick up something basic like Kaplan’s GMAT math workbook. You probably won’t be able to get through the whole thing on top of your studies, but you can make a plan for yourself to get through one topic or chapter a week and just select whatever topics you think you’re weakest on. Or pick two or three books from the
MGMAT book series to get through. Maybe one of their verbal books, depending how comfortable you feel in verbal. Then you could find a 1 or 2 month plan you like and do that from start to finish over the summer. There are other ways you could break up your time; maybe others will have better suggestions.
RE: grades - if you can ask one of your accounting professors for a recommendation, that will help; they’ll be able to explain the grading system at your school, and say that you are doing well relative to your major.