"I was a little sad when father suddenly fell sick."
Translation:Saya agak sedih ketika ayah tiba-tiba sakit.
As mentioned, for "my father" it would have to say "ayahku", but as we already use "saya" the beginning of the sentence, we can't switch to the informal form (aku - ku) halfway through. Besides, it doesn't actually mention whose father it is.
As for "jatuh" - to fall sick is an English impression that might not translate directly into other languages