Answer by Japanese teacher
You can use the above two phrases to express a general sense of unwell.
具合(ぐあい)が悪(わる)い guai ga warui means “ill, sick, not in good shape, malfunction”.
It can be used to refer to people or things. If you are feeling better, then you can say 具合(ぐあい)がいい guai ga ii (in good shape).
On the other hand, 体調(たいちょう) taichoo means “physical condition”. This can only be used to refer to people.