I'm sure of the accuracy of the sentence " I was sound asleep." but can we say I was having sound sleep?
"I had a sound sleep last night".
"I got some sound sleep over the weekend".
"Everyone needs sound sleep for good health".
All of these are good sentences.
'A sleep' is one period of continuous sleep. So using "a" would be better in your case but, at least in AusE, "I was having sound sleep" is a little odd, but not wrong.