If you plan on studying engineering you should have taken math classes through pre-calculus, i.e., Algebra I, Geometry, Algebra II, Trigonometry and Functions. Ideally, you would have started Calculus. However, the standard engineering curriculum assumes that you will start math in university at Calculus I. If you are not yet up to that level then the college would require you to make up the earlier math courses but they wouldn't count toward your degree.
Engineers will usually take Calc I, CalcII, Calc III, Differential Equations, Linear Algebra and possibly more math classes. CS majors differ significantly between universities in the number of math courses required. Some colleges take a very math intensive approach to prepare you for any scientific or engineering application while others focus more on common math applications in programming. You won't know if you can handle the math unless you try. But, you should ask yourself whether you really have an interest in these subjects if you didn't take the additional math or physics while in IBDP.
If you really are interested in engineering or CS don't let anyone discourage you from trying.