Actually can be used in the present, but your second example doesn't make sense. In contexts like these, actually is generally used to contradict something said:
Person 1: You're a doctor, right?
Person 2: Actually, I'm a nurse.
Currently is used to indicate something that is happening now, and actually can be used like that too, so long as it is correcting/contradicting something.
In some cases, actually can be used to mean currently without being contradictory, but usually (in my experience) it is only used like that when the information will be coming as a surprise:
Person 1 (knows Person 2 as drug addict from high school): So, do you have a job?
Person 2: Actually, I'm a lawyer.