Welcome to the forums, miracles.
I'm afraid your sentences are all wrong.
The past perfect (had had) is not suitable for that sentence.
If it's still morning, you need the present perfect (have had), but #2 (if you had numbered them) should continue like this:
'I have had so many interruptions this morning that I have done scarcely any work'.
If it's no longer morning, you need the simple past:
'I had so many interruptions this morning that I scarcely did any work'.
Now try this: type had had in the Google Custom Search box at the top of the page and you'll find links to earlier threads on the correct use of the past perfect.
Student or Learner