Native speakers would not say "I have got (UK) / gotten (US) sick for + duration." You get or become sick at a particular time or gradually, over some time. e.g. I got sick last Tuesday. e.g. I have been (gradually) getting sick for the last few days (and this process may continue) When you think that the process of "getting sick" has reached a certain stage, you might then say "Now, I am sick. I have been sick for one week / since last Saturday". So in summary, the real-life options are: a) "I have been sick for x days" (I am already sick and this is the duration of my sickness so far) - Most common. b) "I have been getting sick for x days" (and this process of becoming sick may continue into the future) - Unusual but correct and would sound OK in specific contexts.

"Gotten sick" means "i have been sick for 2 days at some time in the past." "Been sick" means you are sick now, and have been sick for two days. Although they are similar enough that in some contexts they are interchangeable, ("I feel terrible. This is the 3rd time this year that I have [been/gotten] sick for 2 days").