Part of taking calculus is learning to do calculus to a certain standard of competency. If you find the computations and concepts understandable then I'd bet you are capable of this.

To me it sounds like you just need to develop more speed, more accuracy, better test taking skills and more strategies for checking and fixing mistakes in your work.

The only real way I know to deal with those problems is to just do more practice on them this entails doing more practice problems and practicing in a style similar to how you would actually be tested.

When I took calc 1 the way working practice problems for me looked was to first do the problem without cheating and looking up the answer, then try to check my work on my own as if I was doing a test, then finally look up the answer in the back of the book or wherever. If I was wrong it was usually due to a calculation error so I would go back to find and fix the error and start over whenever that happened. If I was wrong due to an error in understanding I'd read my book, look up videos or articles on the internet, ask tutors, go to office hours and all that other usual stuff when you are struggling to understand something.

In tests I would often check my work on my calculator. Most scientific calculators allow you to store values in variables so things like simple derivatives and limits can often be approximated very quickly by first typing out whatever formula you need with the variables to save in your calculators history then testing out the formula with different values stored in the variables. This allows you to do simple quick numeric tests for accuracy with things like limits and difference quotients. Those kinds of checks won't prove your answer is right and can suffer from weird rounding errors but they can often be good indicators to show you when you are totally wrong.

With a lot of the grindier problems for calculus if you develop enough speed you can often be fast enough to just work all or most test problems twice. This is useful in situations where you don't have a calculator or having one won't help.

Just some thoughts, I'm no expert and the things that worked for me may not be what you need.