It is the same, just some variation.

I was ill is clearly Byl jsem nemocný. Bylo mi špatně is mainly I was sick (as in eaten something bad (stomach ache, vomitting) or motion sickness, or headache or dizziness, not the state of having a disease). It can also mean that you were feeling bad during your illness. So that's why "feeling ill" was accepted and "ill" not.

As to why "feeling cold" is not accepted - I am not sure, but I thing it is just missing so I will add it.

Also note that your report contains You instead of We.