Careers in computer science without maths
I depends on what you mean by a career. For a low level position with not a lot of chance for advancement it would be possible. But almost all CS fields require some fairly deep understanding of at least some parts of mathematics. As user vonbrand notes it is mostly not calculus, though even that can help. 

But one of the big ideas in CS is being able to separate the "simple" algorithms from those that will actually work in practice. You can go a ways with only standard and well known practice, but you won't be in a very good position to make advancements, even in a "career" in programming. 

But some parts of CS require more maths than others. User Interface design, for example, and Human Factors, are more concerned with psychology and physiology than maths. But Algorithms, Machine Learning, Operating Systems, and lots of others, depend on being able to think in some of the same ways that a mathematician does. Logical, rather than empirical, evidence, can be fundamental. 

The other problem, as you probably already know is that most education programs in CS have quite a lot of required maths. If you don't do well in those courses, your overall record may not be strong enough to advance. 

So, perhaps you just need to find a way to deal with learning the maths you need. Tutors can help, especially if they are wise enough to evaluate where your blocks are. Some students need to repeat a lot of things they "should have learned" at an earlier stage, but didn't. A good tutor can help you get past such things, but it might require special insight into learning and into what is most important. But it also takes work (lots of it) on your part. 

And, more important than specific mathematical "facts" is a mathematical way of approaching a problem.