Student or Learner
I became unconscious, then I fell down. So can I say?
I fell down became unconscious. Likewise
I felt giddy, then I fell down.
I fell down felt giddy.
"I fell down and felt giddy" doesn't communicate either of these.
"I fell down because I was giddy" is better. But why not simply say what you mean: "I became unconscious, then I fell down" -- except that this must be reported evidence unless you say, "I became unconscious, and then I must have fallen down, because I woke up on the ground."
Note: feeling giddy is not becoming unconscious, though it can lead to it.