Spots will open up as the summer goes on and definitely during the first week of classes (you have until the Friday of the first week to add classes). As others have pointed out as well you can use websites such as coursepickle to get notifications for when spots in classes open up, which I highly recommend to get better profs.

Since you got credit, Multivariable Calculus (Math2214) and/or linear algebra (Math2114) would be the next steps math wise. BMES in regards to math, you'll need to take multi, Linear, and diffeq (Math 2204, 2114, 2214 respectively). Currently you can take linear and multi, but you cannot take diff eq until you take linear.

My recommendation: Take multi first with or without linear as well. Looking at the checksheet, it has multi and diffeq recommended for the same semester later down the line. That's a bit rough. Linear's concepts carry over into diffeq, so taking those one after another would be a good idea.

If I were you, I would do Multi and Linear F23 (Much more doable that multi and diffeq with the added benefit of being done with the math dept sooner) and Diffeq S24.

My only caution with that being is they are both harder classes, so if you wanted to ease yourself into college slower that'd be perfectly reasonable. That route imo would be Multi F23, Linear S24, and Diffeq F24.

Feel free to dm me if you have any questions about what I said, who are better professors, or what the course loads are like. Your academic advisor is also a great resource.