Thank you for the question. As per the main question which is your subject title, the answer is no, you should not be taking prednisolone for cystic acne. It might temporarily bring down the inflammation in acne, but it is not a long lasting solution and can worsen your condition.
Are you certain you are suffering from cystic acne? A picture would help us diagnose you better.
I feel that you will benefit from a skin consult definitely to diagnose the rash and give you a long term solution. This involves a detailed consult, physical check, and possibly complementary tests.
Long term oral prednisolone (even though you are on a low dose now) is usually accompanied with undesirable side effects such as lowered immunity, thin skin and weight gain – and should be avoided if your rash does not warrant it.
Hope this helps!