Actually, "being sick" has the implication of 'throwing up', as in "During the entire boat trip, John was being sick," or "I was being sick all over the table". "I have been sick" means that you have been unwell, or ill, due to a disease.
They're both perfectly alright, they just mean differently.
Edit: In lieu of Rolfer's change of question:
Let's take the adjective "happy". The two examples are now "I have been happy" and "I have been being happy".
The first of the two sentences means that you were happy in times past. You might not necessarily be happy now, but you were happy before.
The second of the sentences however, meant that you have been doing some activity which occurs when you are happy, for example, Dancing, or jumping, or shouting, or singing, etc. "I have been being happy" denotes that you were doing an action associated with happiness. This can also be seen by "sick", or "angry" ('being angry' could mean stamping your foot, shouting, saying bad things, etc.).
Essentially, they mean the same thing, just stating it in a different way.
Best Answer
The correct sentence is:
Playing to something is what you do with a talent to something else, normally a person or group of people, for example:
Doing something since something works for events or milestones, e.g:
And yes you can say