No matter what your choice be, you can append ようです or そうです, the sentence will be grammatically perfect. What is important here is the context.
indicates that the speaker talks about himself, otherwise, the statement should be less direct. Thus the fact that the fever cooled is first-hand information from the speaker, he describes his state (that is what ようです is for: describing a state) whereas そうです when appended to a 終止形 indicates rumor (it seems that, it is said that, ...) not to be mixed up with the そうです that clip itself on the 連用形 and express also a state (in the same way as ようです).
To sum up, here the speaker describes a first-hand fact, thus he can't use そうです here, ようです is the correct answer.
EDIT: As pointed out by chocolate, よう・そう would rather connect to さがった rather than さがりました.